Atlas › Modular forms › Weight 2 › Level 934 › 934.2.a

Newspace 934.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(934))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
934.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + O(q^{8})$	+ +	$-1$	934a1 rank 1
934.2.a.b	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} + 3q^{5} + q^{6} + 2q^{7} + O(q^{8})$	− +	$+1$	934b1 rank 0
934.2.a.c	1	$\mathbb{Q}$	$q + q^{2} + 3q^{3} + q^{4} - q^{5} + 3q^{6} - 2q^{7} + O(q^{8})$	− +	$+1$	934c1 rank 0
934.2.a.d	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	− −	$-1$
934.2.a.e	3	degree 3	$3q - 3q^{2} - q^{3} + 3q^{4} - 5q^{5} + q^{6} + 3q^{7} + O(q^{8})$	+ +	$-1$
934.2.a.f	3	degree 3	$3q + 3q^{2} - q^{3} + 3q^{4} - 3q^{5} - q^{6} - 3q^{7} + O(q^{8})$	− −	$-1$
934.2.a.g	4	degree 4	$4q - 4q^{2} + 4q^{4} - 3q^{5} + 3q^{7} + O(q^{8})$	+ +	$-1$
934.2.a.h	11	degree 11	$11q - 11q^{2} - q^{3} + 11q^{4} + 10q^{5} + q^{6} - 4q^{7} + O(q^{8})$	+ −	$+1$
934.2.a.i	12	degree 12	$12q + 12q^{2} + 2q^{3} + 12q^{4} + 4q^{5} + 2q^{6} + 7q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5}$ 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 $T$
934.2.a.a	$x - 4$
934.2.a.b	$x - 10$
934.2.a.c	$x$
934.2.a.d	$x^{2} + 8x + 14$
934.2.a.e	$x^{3} + 16x^{2} + 29x - 155$
934.2.a.f	$x^{3} + 10x^{2} - 11x - 223$
934.2.a.g	$x^{4} + 9x^{3} - 40x^{2} - 329x - 228$
934.2.a.h	$x^{11} - 29x^{10} + 90x^{9} + 3966x^{8} - 30446x^{7} - 117986x^{6} + 1539197x^{5} - 1670727x^{4} - 16481192x^{3} + 42989003x^{2} + 813258x - 56603578$
934.2.a.i	$x^{12} - 14x^{11} - 327x^{10} + 5363x^{9} + 21275x^{8} - 551448x^{7} + 519887x^{6} + 15373994x^{5} - 26074383x^{4} - 121856300x^{3} + 184009938x^{2} + 133658994x - 185076529$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(934))$	38
Old forms	78
Cusp forms $S_{2}(\Gamma_0(934))$	116
Eisenstein series $E_{2}(\Gamma_0(934))$	3
Modular forms $M_{2}(\Gamma_0(934))$	119

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(934)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(467))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.304 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, 467, 934]: [0, 1, 40, 119] (certified at ell = 2147483179)
T = [(3, 1), (5, 3)]; h of degree 38 = 1 x 38 (phi(ord eps) x dim S_k^new); 6 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(934, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 934:2 1000

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