Atlas › Modular forms › Weight 2 › Level 962 › 962.2.a

Newspace 962.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(962))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
962.2.a.a	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 2q^{5} - 2q^{7} + O(q^{8})$	− − −	$+1$	962a1 rank 0
962.2.a.b	2	$\mathbb{Q}(\sqrt{5})$	$2q + 2q^{2} - q^{3} + 2q^{4} - 2q^{5} - q^{6} - 5q^{7} + O(q^{8})$	− − +	$-1$
962.2.a.c	2	$\mathbb{Q}(\sqrt{5})$	$2q + 2q^{2} - q^{3} + 2q^{4} - 2q^{5} - q^{6} - 3q^{7} + O(q^{8})$	− + −	$-1$
962.2.a.d	2	$\mathbb{Q}(\sqrt{13})$	$2q + 2q^{2} + q^{3} + 2q^{4} - 6q^{5} + q^{6} + 5q^{7} + O(q^{8})$	− − −	$+1$
962.2.a.e	3	degree 3	$3q - 3q^{2} - 3q^{3} + 3q^{4} + 2q^{5} + 3q^{6} - 5q^{7} + O(q^{8})$	+ + +	$-1$
962.2.a.f	4	degree 4	$4q - 4q^{2} - 3q^{3} + 4q^{4} + 3q^{6} - 9q^{7} + O(q^{8})$	+ − −	$-1$
962.2.a.g	4	degree 4	$4q + 4q^{2} + q^{3} + 4q^{4} + 8q^{5} + q^{6} + 3q^{7} + O(q^{8})$	− − −	$+1$
962.2.a.h	5	degree 5	$5q - 5q^{2} + 5q^{4} - 2q^{5} + 6q^{7} + O(q^{8})$	+ + −	$+1$
962.2.a.i	5	degree 5	$5q - 5q^{2} + 5q^{4} + 2q^{5} + 10q^{7} + O(q^{8})$	+ − +	$+1$
962.2.a.j	7	degree 7	$7q + 7q^{2} + 6q^{3} + 7q^{4} + 4q^{5} + 6q^{6} + 8q^{7} + O(q^{8})$	− + +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5} + 5T_{7} + 7T_{11} + 9T_{17}$ 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 $T$
962.2.a.a	$x - 56$
962.2.a.b	$x^{2} + 73x + 671$
962.2.a.c	$x^{2} + 59x + 769$
962.2.a.d	$x^{2} - 23x - 1587$
962.2.a.e	$x^{3} - 15x^{2} - 1483x - 15956$
962.2.a.f	$x^{4} + 31x^{3} - 4697x^{2} - 44512x + 4174748$
962.2.a.g	$x^{4} - 38x^{3} - 3345x^{2} + 112489x + 1219816$
962.2.a.h	$x^{5} - 109x^{4} - 2340x^{3} + 528438x^{2} - 15297486x + 103077235$
962.2.a.i	$x^{5} - x^{4} - 5074x^{3} + 26716x^{2} + 5288832x - 3098087$
962.2.a.j	$x^{7} - 177x^{6} + 8620x^{5} + 116348x^{4} - 19978002x^{3} + 457713727x^{2} - 522754196x - 53735943172$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(962))$	35
Old forms	94
Cusp forms $S_{2}(\Gamma_0(962))$	129
Eisenstein series $E_{2}(\Gamma_0(962))$	7
Modular forms $M_{2}(\Gamma_0(962))$	136

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(962)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(26))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(37))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(74))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(481))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.477 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, 13, 26, 37, 74, 481, 962]: [0, 1, 1, 5, 3, 11, 44, 136] (certified at ell = 2147483629)
T = [(3, 1), (5, 3), (7, 5), (11, 7), (17, 9)]; h of degree 35 = 1 x 35 (phi(ord eps) x dim S_k^new); 9 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(962, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 962:2 1000

← 961.2.a · 963.2.a →