Atlas › Modular forms › Weight 2 › Level 452 › 452.2.a

Newspace 452.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(452))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
452.2.a.a	3	degree 3	$3q - 3q^{3} - 3q^{5} + O(q^{8})$	−
452.2.a.b	7	degree 7	$7q + 3q^{3} + 3q^{5} + O(q^{8})$	+

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 $T$
452.2.a.a	$x^{3} + 6x^{2} + 9x + 3$
452.2.a.b	$x^{7} - 6x^{6} - 27x^{5} + 207x^{4} - 28x^{3} - 1440x^{2} + 2246x - 926$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(452))$	10
Old forms	45
Cusp forms $S_{2}(\Gamma_0(452))$	55
Eisenstein series $E_{2}(\Gamma_0(452))$	5
Modular forms $M_{2}(\Gamma_0(452))$	60

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(452)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(113))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(226))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.195 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, 4, 113, 226, 452]: [0, 1, 2, 10, 30, 60] (certified at ell = 2147480161)
T = [(3, 1), (5, 1)]; h of degree 10 = 1 x 10 (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(452, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 452:2 1000

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