Atlas › Modular forms › Weight 2 › Level 227 › 227.2.a

Newspace 227.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(227))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
227.2.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q - 4q^{3} - 2q^{7} + O(q^{8})$	+	$-1$
227.2.a.b	2	$\mathbb{Q}(\sqrt{5})$	$2q + 3q^{3} + 6q^{4} - 4q^{5} - 5q^{6} + 7q^{7} + O(q^{8})$	−	$+1$
227.2.a.c	2	$\mathbb{Q}(\sqrt{29})$	$2q + 2q^{2} - q^{3} - 2q^{4} + 4q^{5} - q^{6} + 3q^{7} + O(q^{8})$	−	$+1$
227.2.a.d	3	degree 3	$3q - 2q^{2} + q^{3} - 5q^{5} - 3q^{6} - 6q^{7} + O(q^{8})$	+	$-1$
227.2.a.e	10	degree 10	$10q + q^{3} + 14q^{4} + 7q^{5} + 3q^{6} + O(q^{8})$	−	$+1$

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 $T$
227.2.a.a	$x^{2} + 4x + 2$
227.2.a.b	$x^{2} - 3x + 1$
227.2.a.c	$x^{2} - x - 7$
227.2.a.d	$x^{3} + x^{2} - 2x - 1$
227.2.a.e	$x^{10} - x^{9} - 37x^{8} + 24x^{7} + 473x^{6} - 218x^{5} - 2390x^{4} + 1349x^{3} + 4078x^{2} - 3704x + 706$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(227))$	19
Old forms	0
Cusp forms $S_{2}(\Gamma_0(227))$	19
Eisenstein series $E_{2}(\Gamma_0(227))$	1
Modular forms $M_{2}(\Gamma_0(227))$	20

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.17 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, 227]: [0, 20] (certified at ell = 2147479573)
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(227, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 227:2 1000

← 226.2.a · 228.2.a →