Atlas › Modular forms › Weight 10 › Level 23 › 23.10.a

Newspace 23.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(23))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
23.10.a.a	7	degree 7	$7q - 89q^{3} + 1536q^{4} - 2388q^{5} - 12518q^{6} - 9896q^{7} + O(q^{8})$	+	$-1$
23.10.a.b	10	degree 10	$10q + 32q^{2} + 235q^{3} + 3072q^{4} + 112q^{5} + 10975q^{6} + 1280q^{7} + O(q^{8})$	−	$+1$

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 $T$
23.10.a.a	$x^{7} + 89x^{6} - 71504x^{5} - 5546334x^{4} + 1158288801x^{3} + 55414954997x^{2} - 4635970367970x - 144096569656160$
23.10.a.b	$x^{10} - 267x^{9} - 103682x^{8} + 26353971x^{7} + 3516518700x^{6} - 803320657895x^{5} - 44713801674326x^{4} + 8700567080461209x^{3} + 171415439287597043x^{2} - 30934047659899510490x + 104637151790735845176$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(23))$	17
Old forms	0
Cusp forms $S_{10}(\Gamma_0(23))$	17
Eisenstein series $E_{10}(\Gamma_0(23))$	2
Modular forms $M_{10}(\Gamma_0(23))$	19

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.301 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, 23]: [1, 19] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 17 = 1 x 17 (phi(ord eps) x dim S_k^new); 5 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(23, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 23:10 1000

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