Atlas › Modular forms › Weight 10 › Level 5 › 5.10.a

Newspace 5.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(5))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
5.10.a.a	1	$\mathbb{Q}$	$q - 8q^{2} - 114q^{3} - 448q^{4} - 625q^{5} + 912q^{6} + 4242q^{7} + O(q^{8})$	+	$-1$
5.10.a.b	2	$\mathbb{Q}(\sqrt{1009})$	$2q - 10q^{2} + 260q^{3} + 1044q^{4} + 1250q^{5} - 5336q^{6} + 1700q^{7} + O(q^{8})$	−	$+1$

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 $T$
5.10.a.a	$x + 122$
5.10.a.b	$x^{2} - 250x + 14616$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(5))$	3
Old forms	0
Cusp forms $S_{10}(\Gamma_0(5))$	3
Eisenstein series $E_{10}(\Gamma_0(5))$	2
Modular forms $M_{10}(\Gamma_0(5))$	5

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.263 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, 5]: [1, 5] (certified at ell = 2147483629)
T = [(2, 1), (3, 1)]; h of degree 3 = 1 x 3 (phi(ord eps) x dim S_k^new); 1 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(5, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 5:10 1000

← 4.10.a · 6.10.a →