Atlas › Modular forms › Weight 2 › Level 953 › 953.2.a

Newspace 953.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(953))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
953.2.a.a	32	degree 32	$32q - 5q^{2} - 16q^{3} + 17q^{4} - 6q^{5} - 5q^{6} - 38q^{7} + O(q^{8})$	+	$-1$
953.2.a.b	47	degree 47	$47q + 2q^{2} + 16q^{3} + 58q^{4} + 6q^{5} + 5q^{6} + 42q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
953.2.a.a	$x^{32} + 21x^{31} + 126x^{30} - 292x^{29} - 5821x^{28} - 11546x^{27} + 90473x^{26} + 378191x^{25} - 559356x^{24} - 4896184x^{23} - 658815x^{22} + 36031053x^{21} + 33252387x^{20} - 167349217x^{19} - 241055128x^{18} + 514504223x^{17} + 954619838x^{16} - 1077199086x^{15} - 2400280738x^{14} + 1573736320x^{13} + 4011005237x^{12} - 1656382724x^{11} - 4489790960x^{10} + 1312298637x^{9} + 3299193981x^{8} - 805688820x^{7} - 1503207823x^{6} + 364590009x^{5} + 372378859x^{4} - 102186390x^{3} - 34079546x^{2} + 12176560x - 902775$
953.2.a.b	$x^{47} - 18x^{46} - 18x^{45} + 2146x^{44} - 7913x^{43} - 104427x^{42} + 678502x^{41} + 2497019x^{40} - 27171719x^{39} - 20264017x^{38} + 661517002x^{37} - 498976637x^{36} - 10717271086x^{35} + 18871884979x^{34} + 120346616553x^{33} - 314504747578x^{32} - 951460918787x^{31} + 3357637138438x^{30} + 5265326195264x^{29} - 25209116486996x^{28} - 19590241759870x^{27} + 138459050715994x^{26} + 42240744061941x^{25} - 567339505543125x^{24} - 9481995185660x^{23} + 1749904815099402x^{22} - 265204466297502x^{21} - 4066389382943764x^{20} + 954266383041472x^{19} + 7066993881563239x^{18} - 1810989461789825x^{17} - 9030432179800878x^{16} + 2136263861580523x^{15} + 8245494187098665x^{14} - 1609524352119399x^{13} - 5158697860670231x^{12} + 771944398025902x^{11} + 2086539528036078x^{10} - 231502306795514x^{9} - 500878805032725x^{8} + 41178267666528x^{7} + 62059869679044x^{6} - 3672563919373x^{5} - 3120841055222x^{4} + 112160729169x^{3} + 19062661431x^{2} - 16630723x - 10339$

Orbit

Characteristic polynomial of

T

953.2.a.a

x^{32} + 21x^{31} + 126x^{30} - 292x^{29} - 5821x^{28} - 11546x^{27} + 90473x^{26} + 378191x^{25} - 559356x^{24} - 4896184x^{23} - 658815x^{22} + 36031053x^{21} + 33252387x^{20} - 167349217x^{19} - 241055128x^{18} + 514504223x^{17} + 954619838x^{16} - 1077199086x^{15} - 2400280738x^{14} + 1573736320x^{13} + 4011005237x^{12} - 1656382724x^{11} - 4489790960x^{10} + 1312298637x^{9} + 3299193981x^{8} - 805688820x^{7} - 1503207823x^{6} + 364590009x^{5} + 372378859x^{4} - 102186390x^{3} - 34079546x^{2} + 12176560x - 902775

953.2.a.b

x^{47} - 18x^{46} - 18x^{45} + 2146x^{44} - 7913x^{43} - 104427x^{42} + 678502x^{41} + 2497019x^{40} - 27171719x^{39} - 20264017x^{38} + 661517002x^{37} - 498976637x^{36} - 10717271086x^{35} + 18871884979x^{34} + 120346616553x^{33} - 314504747578x^{32} - 951460918787x^{31} + 3357637138438x^{30} + 5265326195264x^{29} - 25209116486996x^{28} - 19590241759870x^{27} + 138459050715994x^{26} + 42240744061941x^{25} - 567339505543125x^{24} - 9481995185660x^{23} + 1749904815099402x^{22} - 265204466297502x^{21} - 4066389382943764x^{20} + 954266383041472x^{19} + 7066993881563239x^{18} - 1810989461789825x^{17} - 9030432179800878x^{16} + 2136263861580523x^{15} + 8245494187098665x^{14} - 1609524352119399x^{13} - 5158697860670231x^{12} + 771944398025902x^{11} + 2086539528036078x^{10} - 231502306795514x^{9} - 500878805032725x^{8} + 41178267666528x^{7} + 62059869679044x^{6} - 3672563919373x^{5} - 3120841055222x^{4} + 112160729169x^{3} + 19062661431x^{2} - 16630723x - 10339

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(953))$	79
Old forms	0
Cusp forms $S_{2}(\Gamma_0(953))$	79
Eisenstein series $E_{2}(\Gamma_0(953))$	1
Modular forms $M_{2}(\Gamma_0(953))$	80

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.303 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks

dim M^+ at levels [1, 953]: [0, 80] (certified at ell = 2147477809)
T = [(2, 1), (3, 1)]; h of degree 79 = 1 x 79 (phi(ord eps) x dim S_k^new); 8 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(953, 2)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 953:2 1000

← 952.2.a · 954.2.a →