Atlas › Modular forms › Weight 2 › Level 947 › 947.2.a

Newspace 947.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(947))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
947.2.a.a	35	degree 35	$35q - 7q^{2} - 10q^{3} + 29q^{4} - 19q^{5} - 12q^{6} - 27q^{7} + O(q^{8})$	+	$-1$
947.2.a.b	44	degree 44	$44q + 5q^{2} + 8q^{3} + 47q^{4} + 17q^{5} + 25q^{7} + O(q^{8})$	−	$+1$

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 $T$
947.2.a.a	$x^{35} + 17x^{34} + 40x^{33} - 811x^{32} - 4476x^{31} + 13458x^{30} + 133271x^{29} - 47199x^{28} - 2099196x^{27} - 1509922x^{26} + 20645358x^{25} + 26859030x^{24} - 136437160x^{23} - 226747796x^{22} + 628836461x^{21} + 1194216022x^{20} - 2055317651x^{19} - 4228980814x^{18} + 4771106625x^{17} + 10344630714x^{16} - 7773949026x^{15} - 17581147702x^{14} + 8672190478x^{13} + 20576845559x^{12} - 6359400028x^{11} - 16195376277x^{10} + 2880121529x^{9} + 8208108487x^{8} - 743498169x^{7} - 2488107808x^{6} + 113475987x^{5} + 397190632x^{4} - 17346268x^{3} - 26074304x^{2} + 1610826x + 196541$
947.2.a.b	$x^{44} - 13x^{43} - 72x^{42} + 1591x^{41} - 11x^{40} - 84262x^{39} + 173142x^{38} + 2542193x^{37} - 8545869x^{36} - 48127444x^{35} + 221046249x^{34} + 587062161x^{33} - 3669984532x^{32} - 4409040707x^{31} + 42068169741x^{30} + 15001975094x^{29} - 344718106408x^{28} + 62704450538x^{27} + 2055276296520x^{26} - 1116829942411x^{25} - 8984984232243x^{24} + 7108728396272x^{23} + 28815453432938x^{22} - 27611869445350x^{21} - 67404277866877x^{20} + 71504403689829x^{19} + 113621357279878x^{18} - 125430387648463x^{17} - 135412470920748x^{16} + 146702748815661x^{15} + 110941471241648x^{14} - 109691676225083x^{13} - 59830040514226x^{12} + 48695793831709x^{11} + 19625751075384x^{10} - 11483615907741x^{9} - 3318717954016x^{8} + 1320251232422x^{7} + 244078868143x^{6} - 74350870868x^{5} - 6684581655x^{4} + 1910409948x^{3} + 25803437x^{2} - 15185807x + 446357$

Orbit

Characteristic polynomial of

T

947.2.a.a

x^{35} + 17x^{34} + 40x^{33} - 811x^{32} - 4476x^{31} + 13458x^{30} + 133271x^{29} - 47199x^{28} - 2099196x^{27} - 1509922x^{26} + 20645358x^{25} + 26859030x^{24} - 136437160x^{23} - 226747796x^{22} + 628836461x^{21} + 1194216022x^{20} - 2055317651x^{19} - 4228980814x^{18} + 4771106625x^{17} + 10344630714x^{16} - 7773949026x^{15} - 17581147702x^{14} + 8672190478x^{13} + 20576845559x^{12} - 6359400028x^{11} - 16195376277x^{10} + 2880121529x^{9} + 8208108487x^{8} - 743498169x^{7} - 2488107808x^{6} + 113475987x^{5} + 397190632x^{4} - 17346268x^{3} - 26074304x^{2} + 1610826x + 196541

947.2.a.b

x^{44} - 13x^{43} - 72x^{42} + 1591x^{41} - 11x^{40} - 84262x^{39} + 173142x^{38} + 2542193x^{37} - 8545869x^{36} - 48127444x^{35} + 221046249x^{34} + 587062161x^{33} - 3669984532x^{32} - 4409040707x^{31} + 42068169741x^{30} + 15001975094x^{29} - 344718106408x^{28} + 62704450538x^{27} + 2055276296520x^{26} - 1116829942411x^{25} - 8984984232243x^{24} + 7108728396272x^{23} + 28815453432938x^{22} - 27611869445350x^{21} - 67404277866877x^{20} + 71504403689829x^{19} + 113621357279878x^{18} - 125430387648463x^{17} - 135412470920748x^{16} + 146702748815661x^{15} + 110941471241648x^{14} - 109691676225083x^{13} - 59830040514226x^{12} + 48695793831709x^{11} + 19625751075384x^{10} - 11483615907741x^{9} - 3318717954016x^{8} + 1320251232422x^{7} + 244078868143x^{6} - 74350870868x^{5} - 6684581655x^{4} + 1910409948x^{3} + 25803437x^{2} - 15185807x + 446357

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(947))$	79
Old forms	0
Cusp forms $S_{2}(\Gamma_0(947))$	79
Eisenstein series $E_{2}(\Gamma_0(947))$	1
Modular forms $M_{2}(\Gamma_0(947))$	80

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.293 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, 947]: [0, 80] (certified at ell = 2147481491)
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(947, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 947:2 1000

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