Atlas › Modular forms › Weight 4 › Level 73 › 73.4.a

Newspace 73.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(73))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
73.4.a.a	1	$\mathbb{Q}$	$q + 3q^{2} - 8q^{3} + q^{4} + 6q^{5} - 24q^{6} - 34q^{7} + O(q^{8})$	−	$-1$
73.4.a.b	7	degree 7	$7q - 12q^{2} - 6q^{3} + 22q^{4} - 32q^{5} + 14q^{6} - 22q^{7} + O(q^{8})$	−	$-1$
73.4.a.c	10	degree 10	$10q + 7q^{2} + 10q^{3} + 47q^{4} + 24q^{5} + 14q^{6} + 42q^{7} + O(q^{8})$	+	$+1$

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 $T$
73.4.a.a	$x + 5$
73.4.a.b	$x^{7} + 18x^{6} - 713x^{4} - 1303x^{3} + 5484x^{2} + 10582x - 2405$
73.4.a.c	$x^{10} - 17x^{9} - 146x^{8} + 3411x^{7} + 2032x^{6} - 211843x^{5} + 354206x^{4} + 4367265x^{3} - 11777829x^{2} - 11176992x + 26451576$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(73))$	18
Old forms	0
Cusp forms $S_{4}(\Gamma_0(73))$	18
Eisenstein series $E_{4}(\Gamma_0(73))$	2
Modular forms $M_{4}(\Gamma_0(73))$	20

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.097 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]: [1, 20] (certified at ell = 2147482873)
T = [(2, 1), (3, 1)]; h of degree 18 = 1 x 18 (phi(ord eps) x dim S_k^new); 3 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, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 73:4 1000

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