Atlas › Modular forms › Weight 4 › Level 190 › 190.4.a

Newspace 190.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(190))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
190.4.a.a	1	$\mathbb{Q}$	$q - 2q^{2} - 2q^{3} + 4q^{4} + 5q^{5} + 4q^{6} + 8q^{7} + O(q^{8})$	+ − −	$+1$
190.4.a.b	1	$\mathbb{Q}$	$q - 2q^{2} + 2q^{3} + 4q^{4} + 5q^{5} - 4q^{6} - 12q^{7} + O(q^{8})$	+ − +	$-1$
190.4.a.c	1	$\mathbb{Q}$	$q + 2q^{2} - 4q^{3} + 4q^{4} + 5q^{5} - 8q^{6} - 20q^{7} + O(q^{8})$	− − −	$-1$
190.4.a.d	2	$\mathbb{Q}(\sqrt{313})$	$2q - 4q^{2} + q^{3} + 8q^{4} + 10q^{5} - 2q^{6} - 27q^{7} + O(q^{8})$	+ − −	$+1$
190.4.a.e	2	$\mathbb{Q}(\sqrt{3})$	$2q - 4q^{2} + 2q^{3} + 8q^{4} - 10q^{5} - 4q^{6} + 8q^{7} + O(q^{8})$	+ + +	$+1$
190.4.a.f	2	$\mathbb{Q}(\sqrt{34})$	$2q + 4q^{2} + 8q^{4} - 10q^{5} + 24q^{7} + O(q^{8})$	− + −	$+1$
190.4.a.g	3	degree 3	$3q - 6q^{2} - q^{3} + 12q^{4} - 15q^{5} + 2q^{6} + q^{7} + O(q^{8})$	+ + −	$-1$
190.4.a.h	3	degree 3	$3q + 6q^{2} - 9q^{3} + 12q^{4} - 15q^{5} - 18q^{6} - 11q^{7} + O(q^{8})$	− + +	$-1$
190.4.a.i	3	degree 3	$3q + 6q^{2} + 11q^{3} + 12q^{4} + 15q^{5} + 22q^{6} + 29q^{7} + O(q^{8})$	− − +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{7}$ 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 $T$
190.4.a.a	$x - 22$
190.4.a.b	$x + 34$
190.4.a.c	$x + 64$
190.4.a.d	$x^{2} + 80x + 348$
190.4.a.e	$x^{2} - 26x - 1154$
190.4.a.f	$x^{2} - 72x - 370$
190.4.a.g	$x^{3} - 2x^{2} - 1702x + 9164$
190.4.a.h	$x^{3} + 42x^{2} - 7742x - 405080$
190.4.a.i	$x^{3} - 98x^{2} + 908x + 58640$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(190))$	18
Old forms	68
Cusp forms $S_{4}(\Gamma_0(190))$	86
Eisenstein series $E_{4}(\Gamma_0(190))$	8
Modular forms $M_{4}(\Gamma_0(190))$	94

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(190)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(5))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(10))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(38))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(95))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.17 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, 2, 5, 10, 19, 38, 95, 190]: [1, 2, 3, 7, 6, 17, 32, 94] (certified at ell = 2147483629)
T = [(3, 1), (7, 3)]; h of degree 18 = 1 x 18 (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(190, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 190:4 1000

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