Atlas › Modular forms › Weight 2 › Level 853 › 853.2.a

Newspace 853.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(853))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
853.2.a.a	33	degree 33	$33q - 13q^{2} - 18q^{3} + 31q^{4} - 16q^{5} - q^{6} - 11q^{7} + O(q^{8})$	+	$-1$
853.2.a.b	37	degree 37	$37q + 13q^{2} + 18q^{3} + 39q^{4} + 14q^{5} + q^{6} + 9q^{7} + O(q^{8})$	−	$+1$

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 $T$
853.2.a.a	$x^{33} + 31x^{32} + 369x^{31} + 1733x^{30} - 2908x^{29} - 66587x^{28} - 210636x^{27} + 483470x^{26} + 4393101x^{25} + 4613272x^{24} - 33397421x^{23} - 93463849x^{22} + 88416285x^{21} + 632343314x^{20} + 258183257x^{19} - 2248267084x^{18} - 2609190771x^{17} + 4442902578x^{16} + 8518590998x^{15} - 4359600982x^{14} - 15142424833x^{13} + 570125987x^{12} + 15939252575x^{11} + 2843177878x^{10} - 10104526924x^{9} - 2470333050x^{8} + 3880825146x^{7} + 768868269x^{6} - 872707215x^{5} - 63076723x^{4} + 93383708x^{3} - 7237746x^{2} - 1093206x + 70811$
853.2.a.b	$x^{37} - 31x^{36} + 347x^{35} - 1023x^{34} - 11731x^{33} + 110290x^{32} - 142113x^{31} - 2256717x^{30} + 10382395x^{29} + 9146433x^{28} - 169755525x^{27} + 251989151x^{26} + 1242206362x^{25} - 4192906312x^{24} - 3018739386x^{23} + 30063608697x^{22} - 17926967106x^{21} - 119985065878x^{20} + 178275701137x^{19} + 262411415246x^{18} - 703067543078x^{17} - 197649999419x^{16} + 1593531989477x^{15} - 472613092140x^{14} - 2185805172089x^{13} + 1528928872933x^{12} + 1724158046259x^{11} - 1952020730939x^{10} - 600163280781x^{9} + 1312492474311x^{8} - 93926017444x^{7} - 442452034977x^{6} + 136091778203x^{5} + 51533196302x^{4} - 29230179920x^{3} + 3188105710x^{2} + 37856504x - 2384633$

Orbit

Characteristic polynomial of

T

853.2.a.a

x^{33} + 31x^{32} + 369x^{31} + 1733x^{30} - 2908x^{29} - 66587x^{28} - 210636x^{27} + 483470x^{26} + 4393101x^{25} + 4613272x^{24} - 33397421x^{23} - 93463849x^{22} + 88416285x^{21} + 632343314x^{20} + 258183257x^{19} - 2248267084x^{18} - 2609190771x^{17} + 4442902578x^{16} + 8518590998x^{15} - 4359600982x^{14} - 15142424833x^{13} + 570125987x^{12} + 15939252575x^{11} + 2843177878x^{10} - 10104526924x^{9} - 2470333050x^{8} + 3880825146x^{7} + 768868269x^{6} - 872707215x^{5} - 63076723x^{4} + 93383708x^{3} - 7237746x^{2} - 1093206x + 70811

853.2.a.b

x^{37} - 31x^{36} + 347x^{35} - 1023x^{34} - 11731x^{33} + 110290x^{32} - 142113x^{31} - 2256717x^{30} + 10382395x^{29} + 9146433x^{28} - 169755525x^{27} + 251989151x^{26} + 1242206362x^{25} - 4192906312x^{24} - 3018739386x^{23} + 30063608697x^{22} - 17926967106x^{21} - 119985065878x^{20} + 178275701137x^{19} + 262411415246x^{18} - 703067543078x^{17} - 197649999419x^{16} + 1593531989477x^{15} - 472613092140x^{14} - 2185805172089x^{13} + 1528928872933x^{12} + 1724158046259x^{11} - 1952020730939x^{10} - 600163280781x^{9} + 1312492474311x^{8} - 93926017444x^{7} - 442452034977x^{6} + 136091778203x^{5} + 51533196302x^{4} - 29230179920x^{3} + 3188105710x^{2} + 37856504x - 2384633

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(853))$	70
Old forms	0
Cusp forms $S_{2}(\Gamma_0(853))$	70
Eisenstein series $E_{2}(\Gamma_0(853))$	1
Modular forms $M_{2}(\Gamma_0(853))$	71

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.263 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, 853]: [0, 71] (certified at ell = 2147481337)
T = [(2, 1), (3, 1)]; h of degree 70 = 1 x 70 (phi(ord eps) x dim S_k^new); 7 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(853, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 853:2 1000

← 852.2.a · 854.2.a →