Atlas › Modular forms › Weight 4 › Level 89 › 89.4.a

Newspace 89.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(89))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
89.4.a.a	1	$\mathbb{Q}$	$q - 4q^{2} - 7q^{3} + 8q^{4} + 11q^{5} + 28q^{6} + 8q^{7} + O(q^{8})$	−	$-1$
89.4.a.b	1	$\mathbb{Q}$	$q - q^{2} + 2q^{3} - 7q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	−	$-1$
89.4.a.c	6	degree 6	$6q - q^{3} + 6q^{4} - 27q^{5} - 71q^{6} - 82q^{7} + O(q^{8})$	−	$-1$
89.4.a.d	14	degree 14	$14q + 3q^{2} + 6q^{3} + 79q^{4} + 6q^{5} + 15q^{6} + 76q^{7} + O(q^{8})$	+	$+1$

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 $T$
89.4.a.a	$x + 11$
89.4.a.b	$x - 1$
89.4.a.c	$x^{6} + x^{5} - 38x^{4} - 62x^{3} + 356x^{2} + 764x + 22$
89.4.a.d	$x^{14} - 9x^{13} - 341x^{12} + 2877x^{11} + 43677x^{10} - 338467x^{9} - 2705301x^{8} + 18711943x^{7} + 86801244x^{6} - 510170688x^{5} - 1404278932x^{4} + 6374836028x^{3} + 9601798072x^{2} - 26943594240x - 10559703312$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(89))$	22
Old forms	0
Cusp forms $S_{4}(\Gamma_0(89))$	22
Eisenstein series $E_{4}(\Gamma_0(89))$	2
Modular forms $M_{4}(\Gamma_0(89))$	24

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.101 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, 89]: [1, 24] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 22 = 1 x 22 (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(89, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 89:4 1000

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