Atlas › Modular forms › Weight 4 › Level 234 › 234.4.a

Newspace 234.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(234))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
234.4.a.a	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} - 17q^{5} - 35q^{7} + O(q^{8})$	+ −
234.4.a.b	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} - 6q^{5} + 20q^{7} + O(q^{8})$	+ −
234.4.a.c	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} - 4q^{5} + 4q^{7} + O(q^{8})$	+ +
234.4.a.d	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} + 2q^{5} - 26q^{7} + O(q^{8})$	+ +
234.4.a.e	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} + 18q^{5} + 20q^{7} + O(q^{8})$	+ −
234.4.a.f	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} + 20q^{5} - 32q^{7} + O(q^{8})$	+ +
234.4.a.g	1	$\mathbb{Q}$	$q + 2q^{2} + 4q^{4} - 11q^{5} + 19q^{7} + O(q^{8})$	− +
234.4.a.h	1	$\mathbb{Q}$	$q + 2q^{2} + 4q^{4} - 10q^{5} - 8q^{7} + O(q^{8})$	− −
234.4.a.i	1	$\mathbb{Q}$	$q + 2q^{2} + 4q^{4} - 2q^{5} - 26q^{7} + O(q^{8})$	− +
234.4.a.j	1	$\mathbb{Q}$	$q + 2q^{2} + 4q^{4} + 16q^{5} - 8q^{7} + O(q^{8})$	− +
234.4.a.k	1	$\mathbb{Q}$	$q + 2q^{2} + 4q^{4} + 16q^{5} + 28q^{7} + O(q^{8})$	− +
234.4.a.l	2	$\mathbb{Q}(\sqrt{22})$	$2q - 4q^{2} + 8q^{4} - 8q^{5} + 12q^{7} + O(q^{8})$	+ −
234.4.a.m	2	$\mathbb{Q}(\sqrt{22})$	$2q + 4q^{2} + 8q^{4} + 8q^{5} + 12q^{7} + O(q^{8})$	− −

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 3T_{7} + 5T_{11} + 7T_{17}$ 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 $T$
234.4.a.a	$x - 1$
234.4.a.b	$x - 144$
234.4.a.c	$x - 40$
234.4.a.d	$x - 520$
234.4.a.e	$x + 144$
234.4.a.f	$x + 116$
234.4.a.g	$x - 593$
234.4.a.h	$x + 1144$
234.4.a.i	$x + 676$
234.4.a.j	$x - 728$
234.4.a.k	$x + 1036$
234.4.a.l	$x^{2} + 584x + 85176$
234.4.a.m	$x^{2} - 656x + 103272$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(234))$	15
Old forms	103
Cusp forms $S_{4}(\Gamma_0(234))$	118
Eisenstein series $E_{4}(\Gamma_0(234))$	16
Modular forms $M_{4}(\Gamma_0(234))$	134

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(234)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(6))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(9))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(13))^{\oplus 6}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(18))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(26))^{\oplus 3}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(39))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(78))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(117))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.366 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, 6, 9, 13, 18, 26, 39, 78, 117, 234]: [1, 2, 2, 5, 4, 5, 11, 13, 16, 46, 44, 130] (certified at ell = 2147483629)
T = [(5, 1), (7, 3), (11, 5), (17, 7)]; h of degree 15 = 1 x 15 (phi(ord eps) x dim S_k^new); 6 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(234, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 234:4 1000

← 233.4.a · 235.4.a →