Atlas › Modular forms › Weight 4 › Level 41 › 41.4.a

Newspace 41.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(41))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
41.4.a.a	3	degree 3	$3q - 3q^{2} - 8q^{3} - 5q^{4} - 10q^{5} - 18q^{6} - 50q^{7} + O(q^{8})$	−	$-1$
41.4.a.b	7	degree 7	$7q + q^{2} + 4q^{3} + 43q^{4} + 10q^{5} + 18q^{6} + 48q^{7} + O(q^{8})$	+	$+1$

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 $T$
41.4.a.a	$x^{3} + 11x^{2} + 33x + 29$
41.4.a.b	$x^{7} - 5x^{6} - 199x^{5} + 1655x^{4} + 2408x^{3} - 49882x^{2} + 125528x - 82714$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(41))$	10
Old forms	0
Cusp forms $S_{4}(\Gamma_0(41))$	10
Eisenstein series $E_{4}(\Gamma_0(41))$	2
Modular forms $M_{4}(\Gamma_0(41))$	12

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.093 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, 41]: [1, 12] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 10 = 1 x 10 (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(41, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 41:4 1000

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