Atlas › Modular forms › Weight 2 › Level 924 › 924.2.a

Newspace 924.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(924))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
924.2.a.a	1	$\mathbb{Q}$	$q - q^{3} - 3q^{5} - q^{7} + O(q^{8})$	+ + +	924a1 rank 0
924.2.a.b	1	$\mathbb{Q}$	$q - q^{3} - q^{5} - q^{7} + O(q^{8})$	+ + −	924b1 rank 1
924.2.a.c	1	$\mathbb{Q}$	$q - q^{3} - q^{5} + q^{7} + O(q^{8})$	+ − +	924c1 rank 1
924.2.a.d	1	$\mathbb{Q}$	$q - q^{3} + q^{5} + q^{7} + O(q^{8})$	+ − −	924d1 rank 0
924.2.a.e	1	$\mathbb{Q}$	$q + q^{3} - 3q^{5} - q^{7} + O(q^{8})$	− + +	924e1 rank 1
924.2.a.f	1	$\mathbb{Q}$	$q + q^{3} - 3q^{5} + q^{7} + O(q^{8})$	− − −	924h1 rank 1
924.2.a.g	1	$\mathbb{Q}$	$q + q^{3} - q^{5} - q^{7} + O(q^{8})$	− + −	924f1 rank 0
924.2.a.h	1	$\mathbb{Q}$	$q + q^{3} + 3q^{5} + q^{7} + O(q^{8})$	− − +	924g1 rank 0

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 2T_{13} + 3T_{17} + 4T_{19} + 5T_{23} + 6T_{29} + 7T_{31} + 8T_{37} + 9T_{41} + 10T_{43} + 11T_{47} + 12T_{53} + 13T_{59} + 14T_{61} + 15T_{67} + 16T_{71}$ 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 $T$
924.2.a.a	$x - 432$
924.2.a.b	$x + 628$
924.2.a.c	$x + 496$
924.2.a.d	$x - 496$
924.2.a.e	$x + 18$
924.2.a.f	$x + 774$
924.2.a.g	$x + 70$
924.2.a.h	$x - 210$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(924))$	8
Old forms	173
Cusp forms $S_{2}(\Gamma_0(924))$	181
Eisenstein series $E_{2}(\Gamma_0(924))$	23
Modular forms $M_{2}(\Gamma_0(924))$	204

Decomposition of the old subspace

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 2.954 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, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924]: [0, 1, 1, 2, 3, 1, 2, 5, 4, 4, 5, 7, 6, 12, 9, 16, 10, 22, 30, 28, 36, 54, 104, 204] (certified at ell = 2147482951)
T = [(5, 1), (13, 2), (17, 3), (19, 4), (23, 5), (29, 6), (31, 7), (37, 8), (41, 9), (43, 10), (47, 11), (53, 12), (59, 13), (61, 14), (67, 15), (71, 16)]; h of degree 8 = 1 x 8 (phi(ord eps) x dim S_k^new); 3 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(924, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 924:2 1000

← 923.2.a · 925.2.a →