Atlas › Modular forms › Weight 6 › Level 73 › 73.6.a

Newspace 73.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(73))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
73.6.a.a	14	degree 14	$14q - 17q^{2} - 35q^{3} + 191q^{4} - 129q^{5} - 202q^{6} - 294q^{7} + O(q^{8})$	+	$-1$
73.6.a.b	16	degree 16	$16q + 15q^{2} + 37q^{3} + 287q^{4} + 121q^{5} - 58q^{6} + 392q^{7} + O(q^{8})$	−	$+1$

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 $T$
73.6.a.a	$x^{14} + 52x^{13} - 792x^{12} - 63814x^{11} + 206629x^{10} + 29295414x^{9} - 37695889x^{8} - 5848943222x^{7} + 6163884278x^{6} + 490288333814x^{5} - 348558593935x^{4} - 16667483243784x^{3} + 3314366677392x^{2} + 184128304907988x + 15823968485868$
73.6.a.b	$x^{16} - 52x^{15} - 1664x^{14} + 115686x^{13} + 740777x^{12} - 101034638x^{11} + 128065667x^{10} + 45024704978x^{9} - 197074281950x^{8} - 11049054393398x^{7} + 61820829381933x^{6} + 1477225985293620x^{5} - 8576138184606820x^{4} - 96921398753645940x^{3} + 520354175701890264x^{2} + 2249590278177577296x - 10051589695790698464$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(73))$	30
Old forms	0
Cusp forms $S_{6}(\Gamma_0(73))$	30
Eisenstein series $E_{6}(\Gamma_0(73))$	2
Modular forms $M_{6}(\Gamma_0(73))$	32

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.241 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, 32] (certified at ell = 2147482873)
T = [(2, 1), (3, 1)]; h of degree 30 = 1 x 30 (phi(ord eps) x dim S_k^new); 6 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, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 73:6 1000

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