Atlas › Modular forms › Weight 8 › Level 41 › 41.8.a

Newspace 41.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(41))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
41.8.a.a	10	degree 10	$10q - q^{2} - 68q^{3} + 383q^{4} - 320q^{5} - 810q^{6} - 2402q^{7} + O(q^{8})$	−	$-1$
41.8.a.b	14	degree 14	$14q + 15q^{2} + 40q^{3} + 1151q^{4} + 180q^{5} + 486q^{6} + 2400q^{7} + O(q^{8})$	+	$+1$

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 $T$
41.8.a.a	$x^{10} + 69x^{9} - 10301x^{8} - 430245x^{7} + 39105926x^{6} + 674518644x^{5} - 52479598612x^{4} - 344946178524x^{3} + 19187946246876x^{2} + 147581505587540x - 240107011681600$
41.8.a.b	$x^{14} - 55x^{13} - 21853x^{12} + 952695x^{11} + 182466162x^{10} - 6227922310x^{9} - 742930945668x^{8} + 19166332130180x^{7} + 1567989571683480x^{6} - 27127638718934720x^{5} - 1665923954462977716x^{4} + 12903019010882456340x^{3} + 745301155823493375208x^{2} + 1816753746218525801400x - 41940721579072236102576$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(41))$	24
Old forms	0
Cusp forms $S_{8}(\Gamma_0(41))$	24
Eisenstein series $E_{8}(\Gamma_0(41))$	2
Modular forms $M_{8}(\Gamma_0(41))$	26

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.275 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, 26] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 24 = 1 x 24 (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(41, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 41:8 1000

← 40.8.a · 42.8.a →