Atlas › Modular forms › Weight 2 › Level 73 › 73.2.a

Newspace 73.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(73))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
73.2.a.a	1	$\mathbb{Q}$	$q + q^{2} - q^{4} + 2q^{5} + 2q^{7} + O(q^{8})$	−	$+1$	73a1 rank 0
73.2.a.b	2	$\mathbb{Q}(\sqrt{5})$	$2q - 3q^{2} - 3q^{3} + 3q^{4} - 3q^{5} + 2q^{6} - 6q^{7} + O(q^{8})$	+	$-1$
73.2.a.c	2	$\mathbb{Q}(\sqrt{13})$	$2q + q^{2} + q^{3} + 3q^{4} - q^{5} - 6q^{6} - 2q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ 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 $T$
73.2.a.a	$x - 1$
73.2.a.b	$x^{2} + 12x + 31$
73.2.a.c	$x^{2} - 4x - 9$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(73))$	5
Old forms	0
Cusp forms $S_{2}(\Gamma_0(73))$	5
Eisenstein series $E_{2}(\Gamma_0(73))$	1
Modular forms $M_{2}(\Gamma_0(73))$	6

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.181 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, 73]: [0, 6] (certified at ell = 2147482873)
T = [(2, 1), (3, 3)]; h of degree 5 = 1 x 5 (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(73, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 73:2 1000

← 72.2.a · 74.2.a →