Atlas › Modular forms › Weight 2 › Level 454 › 454.2.a

Newspace 454.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(454))$

Newforms

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

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
454.2.a.a	$x^{2} + 5x + 5$
454.2.a.b	$x^{4} + 6x^{3} - x^{2} - 30x - 25$
454.2.a.c	$x^{5} - 2x^{4} - 26x^{3} + 60x^{2} + 33x - 19$
454.2.a.d	$x^{7} - 3x^{6} - 31x^{5} + 132x^{4} + 41x^{3} - 612x^{2} + 130x + 853$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(454))$	18
Old forms	38
Cusp forms $S_{2}(\Gamma_0(454))$	56
Eisenstein series $E_{2}(\Gamma_0(454))$	3
Modular forms $M_{2}(\Gamma_0(454))$	59

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(454)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(227))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.29 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, 227, 454]: [0, 1, 20, 59] (certified at ell = 2147479573)
T = [(3, 1), (5, 1)]; h of degree 18 = 1 x 18 (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(454, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 454:2 1000

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