Atlas › Modular forms › Weight 2 › Level 437 › 437.2.a

Newspace 437.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(437))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
437.2.a.a	1	$\mathbb{Q}$	$q + 2q^{3} - 2q^{4} - q^{5} - 5q^{7} + O(q^{8})$	− −	$-1$	437a1 rank 1
437.2.a.b	1	$\mathbb{Q}$	$q + 2q^{2} + 2q^{3} + 2q^{4} + q^{5} + 4q^{6} - 3q^{7} + O(q^{8})$	+ −	$+1$	437b1 rank 0
437.2.a.c	2	$\mathbb{Q}(\sqrt{5})$	$2q - 2q^{2} - 3q^{3} - 2q^{4} + 2q^{5} + 3q^{6} + q^{7} + O(q^{8})$	+ +	$-1$
437.2.a.d	2	$\mathbb{Q}(\sqrt{2})$	$2q - 4q^{3} - 2q^{5} + 4q^{6} - 2q^{7} + O(q^{8})$	− −	$-1$
437.2.a.e	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{3} + 6q^{4} - 2q^{5} - 5q^{6} - 5q^{7} + O(q^{8})$	− −	$-1$
437.2.a.f	5	degree 5	$5q - q^{2} - 4q^{3} + 5q^{4} - q^{5} - q^{6} - 9q^{7} + O(q^{8})$	+ +	$-1$
437.2.a.g	8	degree 8	$8q + 5q^{3} + 10q^{4} + 2q^{5} - 3q^{6} + 9q^{7} + O(q^{8})$	+ −	$+1$
437.2.a.h	12	degree 12	$12q + 2q^{2} + 7q^{3} + 18q^{4} - q^{5} + 14q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ 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 $T$
437.2.a.a	$x - 6$
437.2.a.b	$x - 8$
437.2.a.c	$x^{2} + 11x + 19$
437.2.a.d	$x^{2} + 12x + 4$
437.2.a.e	$x^{2} + 3x + 1$
437.2.a.f	$x^{5} + 13x^{4} - x^{3} - 350x^{2} - 228x + 8$
437.2.a.g	$x^{8} - 15x^{7} - 40x^{6} + 1251x^{5} - 1222x^{4} - 29411x^{3} + 43307x^{2} + 219484x - 254500$
437.2.a.h	$x^{12} - 23x^{11} + 14x^{10} + 2996x^{9} - 15703x^{8} - 113661x^{7} + 961272x^{6} + 483368x^{5} - 17474995x^{4} + 30757657x^{3} + 34242020x^{2} - 86809372x + 17654544$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(437))$	33
Old forms	6
Cusp forms $S_{2}(\Gamma_0(437))$	39
Eisenstein series $E_{2}(\Gamma_0(437))$	3
Modular forms $M_{2}(\Gamma_0(437))$	42

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(437)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.386 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, 19, 23, 437]: [0, 2, 3, 42] (certified at ell = 2147483647)
T = [(2, 1), (3, 3)]; h of degree 33 = 1 x 33 (phi(ord eps) x dim S_k^new); 5 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(437, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 437:2 1000

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