Atlas › Modular forms › Weight 6 › Level 41 › 41.6.a

Newspace 41.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(41))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
41.6.a.a	6	degree 6	$6q - 5q^{2} - 8q^{3} + 15q^{4} - 68q^{5} - 162q^{6} - 344q^{7} + O(q^{8})$	+	$-1$
41.6.a.b	10	degree 10	$10q + 3q^{2} + 28q^{3} + 207q^{4} + 32q^{5} + 54q^{6} + 342q^{7} + O(q^{8})$	−	$+1$

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 $T$
41.6.a.a	$x^{6} + 13x^{5} - 697x^{4} - 8365x^{3} + 37398x^{2} + 89666x - 289816$
41.6.a.b	$x^{10} - 31x^{9} - 1649x^{8} + 53623x^{7} + 868226x^{6} - 31370036x^{5} - 129178028x^{4} + 6695335084x^{3} - 9444577516x^{2} - 285838618620x + 548524184296$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(41))$	16
Old forms	0
Cusp forms $S_{6}(\Gamma_0(41))$	16
Eisenstein series $E_{6}(\Gamma_0(41))$	2
Modular forms $M_{6}(\Gamma_0(41))$	18

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.22 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, 18] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 16 = 1 x 16 (phi(ord eps) x dim S_k^new); 3 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, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 41:6 1000

← 40.6.a · 42.6.a →