Atlas › Modular forms › Weight 4 › Level 26 › 26.4.a

Newspace 26.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(26))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
26.4.a.a	1	$\mathbb{Q}$	$q - 2q^{2} + 3q^{3} + 4q^{4} + 11q^{5} - 6q^{6} + 19q^{7} + O(q^{8})$	+ +	$+1$
26.4.a.b	1	$\mathbb{Q}$	$q + 2q^{2} - q^{3} + 4q^{4} + 17q^{5} - 2q^{6} - 35q^{7} + O(q^{8})$	− −	$+1$
26.4.a.c	1	$\mathbb{Q}$	$q + 2q^{2} + 4q^{3} + 4q^{4} - 18q^{5} + 8q^{6} + 20q^{7} + O(q^{8})$	− −	$+1$

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 $T$
26.4.a.a	$x - 36$
26.4.a.b	$x - 50$
26.4.a.c	$x + 50$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(26))$	3
Old forms	6
Cusp forms $S_{4}(\Gamma_0(26))$	9
Eisenstein series $E_{4}(\Gamma_0(26))$	4
Modular forms $M_{4}(\Gamma_0(26))$	13

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(26)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(13))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.1 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, 13, 26]: [1, 2, 5, 13] (certified at ell = 2147483629)
T = [(3, 1), (5, 3)]; h of degree 3 = 1 x 3 (phi(ord eps) x dim S_k^new); 1 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(26, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 26:4 1000

← 25.4.a · 27.4.a →