Atlas › Modular forms › Weight 2 › Level 295 › 295.2.a

Newspace 295.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(295))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
295.2.a.a	3	degree 3	$3q - 3q^{2} - 3q^{3} + 3q^{4} + 3q^{5} - 6q^{7} + O(q^{8})$	− −	$-1$
295.2.a.b	3	degree 3	$3q - q^{2} - q^{3} - q^{4} - 3q^{5} - 2q^{6} + O(q^{8})$	+ +	$-1$
295.2.a.c	6	degree 6	$6q + 2q^{2} + q^{3} + 4q^{4} + 6q^{5} - 2q^{6} + 2q^{7} + O(q^{8})$	− +	$+1$
295.2.a.d	7	degree 7	$7q + q^{2} + 3q^{3} + 7q^{4} - 7q^{5} + 8q^{6} - 4q^{7} + O(q^{8})$	+ −	$+1$

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 $T$
295.2.a.a	$x^{3} + 6x^{2} + 9x + 3$
295.2.a.b	$x^{3} + 2x^{2} - x - 1$
295.2.a.c	$x^{6} - 3x^{5} - 14x^{4} + 25x^{3} + 58x^{2} - 50x - 71$
295.2.a.d	$x^{7} - 4x^{6} - 29x^{5} + 119x^{4} + 179x^{3} - 764x^{2} - 137x + 541$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(295))$	19
Old forms	10
Cusp forms $S_{2}(\Gamma_0(295))$	29
Eisenstein series $E_{2}(\Gamma_0(295))$	3
Modular forms $M_{2}(\Gamma_0(295))$	32

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(295)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(59))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.27 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, 5, 59, 295]: [0, 1, 6, 32] (certified at ell = 2147482481)
T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (phi(ord eps) x dim S_k^new); 2 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(295, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 295:2 1000

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