Atlas › Modular forms › Weight 2 › Level 554 › 554.2.a

Newspace 554.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(554))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
554.2.a.a	3	degree 3	$3q + 3q^{2} - 2q^{3} + 3q^{4} - 7q^{5} - 2q^{6} - 6q^{7} + O(q^{8})$	− −	$-1$
554.2.a.b	4	degree 4	$4q - 4q^{2} - 2q^{3} + 4q^{4} + q^{5} + 2q^{6} - 6q^{7} + O(q^{8})$	+ +	$-1$
554.2.a.c	8	degree 8	$8q - 8q^{2} + 3q^{3} + 8q^{4} - 2q^{5} - 3q^{6} + 8q^{7} + O(q^{8})$	+ −	$+1$
554.2.a.d	9	degree 9	$9q + 9q^{2} - q^{3} + 9q^{4} + 8q^{5} - q^{6} + 8q^{7} + O(q^{8})$	− +	$+1$

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 $T$
554.2.a.a	$x^{3} + 23x^{2} + 167x + 377$
554.2.a.b	$x^{4} - x^{3} - 65x^{2} - 235x - 236$
554.2.a.c	$x^{8} + 3x^{7} - 256x^{6} - 392x^{5} + 21579x^{4} + 9862x^{3} - 653091x^{2} + 113591x + 4500503$
554.2.a.d	$x^{9} - 23x^{8} + 4x^{7} + 3282x^{6} - 18449x^{5} - 88146x^{4} + 671467x^{3} + 1172635x^{2} - 7086631x - 13646052$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(554))$	24
Old forms	44
Cusp forms $S_{2}(\Gamma_0(554))$	68
Eisenstein series $E_{2}(\Gamma_0(554))$	3
Modular forms $M_{2}(\Gamma_0(554))$	71

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(554)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(277))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.215 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, 277, 554]: [0, 1, 23, 71] (certified at ell = 2147483137)
T = [(3, 1), (5, 3)]; h of degree 24 = 1 x 24 (phi(ord eps) x dim S_k^new); 4 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(554, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 554:2 1000

← 553.2.a · 555.2.a →