Atlas › Modular forms › Weight 2 › Level 233 › 233.2.a

Newspace 233.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(233))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
233.2.a.a	1	$\mathbb{Q}$	$q + q^{2} - 2q^{3} - q^{4} + 2q^{5} - 2q^{6} + 4q^{7} + O(q^{8})$	−	$+1$	233a1 rank 0
233.2.a.b	7	degree 7	$7q - 2q^{2} - 8q^{3} + 2q^{4} - 3q^{5} - 2q^{6} - 17q^{7} + O(q^{8})$	+	$-1$
233.2.a.c	11	degree 11	$11q - 2q^{2} + 10q^{3} + 14q^{4} - q^{5} - 2q^{6} + 15q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
233.2.a.a	$x + 1$
233.2.a.b	$x^{7} + 10x^{6} + 30x^{5} + 27x^{4} - 11x^{3} - 19x^{2} + 3$
233.2.a.c	$x^{11} - 8x^{10} - 6x^{9} + 195x^{8} - 347x^{7} - 1223x^{6} + 4406x^{5} - 1331x^{4} - 12042x^{3} + 20420x^{2} - 13020x + 2978$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(233))$	19
Old forms	0
Cusp forms $S_{2}(\Gamma_0(233))$	19
Eisenstein series $E_{2}(\Gamma_0(233))$	1
Modular forms $M_{2}(\Gamma_0(233))$	20

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.168 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, 233]: [0, 20] (certified at ell = 2147482481)
T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (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(233, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 233:2 1000

← 232.2.a · 234.2.a →