Atlas › Modular forms › Weight 2 › Level 811 › 811.2.a

Newspace 811.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(811))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
811.2.a.a	1	$\mathbb{Q}$	$q - 2q^{4} + q^{5} + O(q^{8})$	+	$-1$	811a1 rank 1
811.2.a.b	26	degree 26	$26q - 6q^{2} - 4q^{3} + 20q^{4} - 30q^{5} - 11q^{6} - 5q^{7} + O(q^{8})$	+	$-1$
811.2.a.c	40	degree 40	$40q + 6q^{2} + 2q^{3} + 46q^{4} + 33q^{5} + 5q^{6} + 5q^{7} + O(q^{8})$	−	$+1$

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 $T$
811.2.a.a	$x$
811.2.a.b	$x^{26} + 10x^{25} - 18x^{24} - 442x^{23} - 358x^{22} + 8148x^{21} + 13409x^{20} - 83369x^{19} - 168178x^{18} + 524468x^{17} + 1141059x^{16} - 2092609x^{15} - 4649606x^{14} + 5171728x^{13} + 11701444x^{12} - 7131687x^{11} - 18018234x^{10} + 3667494x^{9} + 15976464x^{8} + 2227308x^{7} - 6673453x^{6} - 2956654x^{5} + 432217x^{4} + 548174x^{3} + 138739x^{2} + 14858x + 588$
811.2.a.c	$x^{40} - 8x^{39} - 127x^{38} + 1164x^{37} + 6493x^{36} - 73278x^{35} - 163964x^{34} + 2647143x^{33} + 1660959x^{32} - 61394449x^{31} + 18199710x^{30} + 969455262x^{29} - 854570328x^{28} - 10786219608x^{27} + 13755586801x^{26} + 86319425194x^{25} - 133766956119x^{24} - 502832415848x^{23} + 875961641786x^{22} + 2145003661881x^{21} - 4015308392509x^{20} - 6713584694833x^{19} + 13081748752208x^{18} + 15400191705280x^{17} - 30416756896351x^{16} - 25791164591880x^{15} + 50331633120897x^{14} + 31296173952580x^{13} - 58738036928220x^{12} - 27110201364694x^{11} + 47530721750247x^{10} + 16275710852152x^{9} - 25908161040026x^{8} - 6389832544486x^{7} + 9062203788734x^{6} + 1459725763556x^{5} - 1867948728448x^{4} - 146611677520x^{3} + 190179178848x^{2} + 884814592x - 5457135488$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(811))$	67
Old forms	0
Cusp forms $S_{2}(\Gamma_0(811))$	67
Eisenstein series $E_{2}(\Gamma_0(811))$	1
Modular forms $M_{2}(\Gamma_0(811))$	68

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.264 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, 811]: [0, 68] (certified at ell = 2147478481)
T = [(2, 1), (3, 1)]; h of degree 67 = 1 x 67 (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(811, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 811:2 1000

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