Atlas › Modular forms › Weight 4 › Level 201 › 201.4.a

Newspace 201.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(201))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
201.4.a.a	1	$\mathbb{Q}$	$q - 4q^{2} - 3q^{3} + 8q^{4} - 19q^{5} + 12q^{6} + 13q^{7} + O(q^{8})$	+ −	$-1$
201.4.a.b	6	degree 6	$6q - 5q^{2} + 18q^{3} + 13q^{4} - 12q^{5} - 15q^{6} - 62q^{7} + O(q^{8})$	− +	$-1$
201.4.a.c	7	degree 7	$7q - q^{2} - 21q^{3} + 21q^{4} + 11q^{5} + 3q^{6} - 33q^{7} + O(q^{8})$	+ −	$-1$
201.4.a.d	9	degree 9	$9q + 3q^{2} - 27q^{3} + 45q^{4} + 12q^{5} - 9q^{6} + 8q^{7} + O(q^{8})$	+ +	$+1$
201.4.a.e	11	degree 11	$11q + 3q^{2} + 33q^{3} + 69q^{4} + 8q^{5} + 9q^{6} + 78q^{7} + O(q^{8})$	− −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{5}$ 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 $T$
201.4.a.a	$x + 23$
201.4.a.b	$x^{6} + 17x^{5} - 147x^{4} - 3245x^{3} - 1914x^{2} + 118508x + 360268$
201.4.a.c	$x^{7} - 10x^{6} - 309x^{5} + 2860x^{4} + 29946x^{3} - 240328x^{2} - 867656x + 4880952$
201.4.a.d	$x^{9} - 15x^{8} - 786x^{7} + 8860x^{6} + 185381x^{5} - 1608761x^{4} - 13137808x^{3} + 97439936x^{2} + 137960192x - 785739520$
201.4.a.e	$x^{11} - 11x^{10} - 926x^{9} + 9810x^{8} + 311585x^{7} - 3285113x^{6} - 43769992x^{5} + 492984150x^{4} + 1791118440x^{3} - 28214412416x^{2} + 59618119680x + 1679511552$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(201))$	34
Old forms	32
Cusp forms $S_{4}(\Gamma_0(201))$	66
Eisenstein series $E_{4}(\Gamma_0(201))$	4
Modular forms $M_{4}(\Gamma_0(201))$	70

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(201)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(67))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.138 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, 3, 67, 201]: [1, 2, 18, 70] (certified at ell = 2147483647)
T = [(2, 1), (5, 1)]; h of degree 34 = 1 x 34 (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(201, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 201:4 1000

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