Atlas › Modular forms › Weight 2 › Level 173 › 173.2.a

Newspace 173.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(173))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
173.2.a.a	4	degree 4	$4q - q^{2} - 6q^{3} - q^{4} - q^{5} - 9q^{7} + O(q^{8})$	+	$-1$
173.2.a.b	10	degree 10	$10q + q^{2} + 8q^{3} + 13q^{4} + q^{5} - 6q^{6} + 11q^{7} + O(q^{8})$	−	$+1$

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 $T$
173.2.a.a	$x^{4} + 7x^{3} + 13x^{2} + 7x + 1$
173.2.a.b	$x^{10} - 9x^{9} + 9x^{8} + 123x^{7} - 346x^{6} - 169x^{5} + 1558x^{4} - 1702x^{3} + 322x^{2} + 247x - 41$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(173))$	14
Old forms	0
Cusp forms $S_{2}(\Gamma_0(173))$	14
Eisenstein series $E_{2}(\Gamma_0(173))$	1
Modular forms $M_{2}(\Gamma_0(173))$	15

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.164 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, 173]: [0, 15] (certified at ell = 2147482093)
T = [(2, 1), (3, 1)]; h of degree 14 = 1 x 14 (phi(ord eps) x dim S_k^new); 2 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(173, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 173:2 1000

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