Atlas › Modular forms › Weight 4 › Level 101 › 101.4.a

Newspace 101.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(101))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
101.4.a.a	9	degree 9	$9q - 5q^{2} - 16q^{3} + 7q^{4} - 6q^{5} - 2q^{6} - 39q^{7} + O(q^{8})$	−	$-1$
101.4.a.b	16	degree 16	$16q + q^{2} + 14q^{3} + 91q^{4} + 14q^{5} + 34q^{6} + 45q^{7} + O(q^{8})$	+	$+1$

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 $T$
101.4.a.a	$x^{9} + 21x^{8} + 60x^{7} - 868x^{6} - 3569x^{5} + 7229x^{4} + 33249x^{3} - 24855x^{2} - 81988x + 68542$
101.4.a.b	$x^{16} - 15x^{15} - 343x^{14} + 5509x^{13} + 43505x^{12} - 785215x^{11} - 2580987x^{10} + 56172021x^{9} + 77168921x^{8} - 2193438905x^{7} - 1243893859x^{6} + 46635745257x^{5} + 15893513081x^{4} - 486376478453x^{3} - 224780192032x^{2} + 1721965023226x + 1324386847700$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(101))$	25
Old forms	0
Cusp forms $S_{4}(\Gamma_0(101))$	25
Eisenstein series $E_{4}(\Gamma_0(101))$	2
Modular forms $M_{4}(\Gamma_0(101))$	27

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.103 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, 101]: [1, 27] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 25 = 1 x 25 (phi(ord eps) x dim S_k^new); 4 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(101, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 101:4 1000

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