Atlas › Modular forms › Weight 2 › Level 453 › 453.2.a

Newspace 453.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(453))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
453.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - 3q^{2} + 2q^{3} + 3q^{4} + 3q^{5} - 3q^{6} - 4q^{7} + O(q^{8})$	− +	$+1$
453.2.a.b	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} + 2q^{3} - q^{4} - q^{5} - q^{6} - 6q^{7} + O(q^{8})$	− −	$-1$
453.2.a.c	2	$\mathbb{Q}(\sqrt{3})$	$2q - 2q^{3} + 2q^{4} + 4q^{5} + 2q^{7} + O(q^{8})$	+ −	$+1$
453.2.a.d	2	$\mathbb{Q}(\sqrt{5})$	$2q + 3q^{2} - 2q^{3} + 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + O(q^{8})$	+ −	$+1$
453.2.a.e	3	degree 3	$3q - q^{2} - 3q^{3} - q^{4} - 3q^{5} + q^{6} + 2q^{7} + O(q^{8})$	+ +	$-1$
453.2.a.f	5	degree 5	$5q - 3q^{2} - 5q^{3} + 11q^{4} - 4q^{5} + 3q^{6} - 6q^{7} + O(q^{8})$	+ +	$-1$
453.2.a.g	9	degree 9	$9q + 6q^{2} + 9q^{3} + 12q^{4} - 2q^{5} + 6q^{6} + 14q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{5}$ 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 $T$
453.2.a.a	$x^{2} - 6x - 11$
453.2.a.b	$x^{2} + 4x - 1$
453.2.a.c	$x^{2} - 12x + 33$
453.2.a.d	$x^{2} + 6x - 11$
453.2.a.e	$x^{3} + 10x^{2} - 32x - 328$
453.2.a.f	$x^{5} + 15x^{4} - 27x^{3} - 924x^{2} - 106x + 14341$
453.2.a.g	$x^{9} - 312x^{7} + 63x^{6} + 28690x^{5} - 30335x^{4} - 787221x^{3} + 2013114x^{2} + 720184x - 3455048$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(453))$	25
Old forms	24
Cusp forms $S_{2}(\Gamma_0(453))$	49
Eisenstein series $E_{2}(\Gamma_0(453))$	3
Modular forms $M_{2}(\Gamma_0(453))$	52

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(453)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(151))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.295 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, 3, 151, 453]: [0, 1, 13, 52] (certified at ell = 2147482951)
T = [(2, 1), (5, 3)]; h of degree 25 = 1 x 25 (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(453, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 453:2 1000

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