Atlas › Modular forms › Weight 2 › Level 36 › 36.2.a

Newspace 36.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(36))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
36.2.a.a	1	$\mathbb{Q}$	$q - 4q^{7} + O(q^{8})$			$\mathbb{Q}(\sqrt{-3})$	36a1 rank 0

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + T_{7}$ 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 $T$
36.2.a.a	$x + 4$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(36))$	1
Old forms	0
Cusp forms $S_{2}(\Gamma_0(36))$	1
Eisenstein series $E_{2}(\Gamma_0(36))$	11
Modular forms $M_{2}(\Gamma_0(36))$	12

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.105 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, 9, 12, 18, 36]: [0, 1, 1, 2, 3, 2, 5, 5, 9] (certified at ell = 2147483647)
T = [(5, 1), (7, 1)]; h of degree 1 = 1 x 1 (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(36, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 36:2 1000

← 35.2.a · 37.2.a →