Atlas › Modular forms › Weight 2 › Level 926 › 926.2.a

Newspace 926.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(926))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
926.2.a.a	1	$\mathbb{Q}$	$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + O(q^{8})$	− +	$+1$	926a1 rank 0
926.2.a.b	5	degree 5	$5q - 5q^{2} - q^{3} + 5q^{4} + q^{5} + q^{6} - 3q^{7} + O(q^{8})$	+ +	$-1$
926.2.a.c	5	degree 5	$5q + 5q^{2} - 5q^{3} + 5q^{4} - 5q^{5} - 5q^{6} - 5q^{7} + O(q^{8})$	− −	$-1$
926.2.a.d	13	degree 13	$13q + 13q^{2} + 5q^{3} + 13q^{4} + 7q^{5} + 5q^{6} + 13q^{7} + O(q^{8})$	− +	$+1$
926.2.a.e	15	degree 15	$15q - 15q^{2} + q^{3} + 15q^{4} + q^{5} - q^{6} + 3q^{7} + O(q^{8})$	+ −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
926.2.a.a	$x - 2$
926.2.a.b	$x^{5} - 12x^{3} + 19x^{2} - 8x + 1$
926.2.a.c	$x^{5} + 10x^{4} + 30x^{3} + 27x^{2} - 8x - 13$
926.2.a.d	$x^{13} - 12x^{12} - 4x^{11} + 561x^{10} - 1805x^{9} - 5495x^{8} + 35870x^{7} - 23709x^{6} - 178903x^{5} + 392763x^{4} - 96698x^{3} - 481083x^{2} + 507848x - 146047$
926.2.a.e	$x^{15} - 2x^{14} - 90x^{13} + 145x^{12} + 3049x^{11} - 3983x^{10} - 49364x^{9} + 55473x^{8} + 407809x^{7} - 422215x^{6} - 1705912x^{5} + 1662629x^{4} + 3324548x^{3} - 2964245x^{2} - 2382900x + 1896500$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(926))$	39
Old forms	76
Cusp forms $S_{2}(\Gamma_0(926))$	115
Eisenstein series $E_{2}(\Gamma_0(926))$	3
Modular forms $M_{2}(\Gamma_0(926))$	118

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(926)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(463))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.274 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, 2, 463, 926]: [0, 1, 39, 118] (certified at ell = 2147483647)
T = [(3, 1), (5, 1)]; h of degree 39 = 1 x 39 (phi(ord eps) x dim S_k^new); 5 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(926, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 926:2 1000

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