Atlas › Modular forms › Weight 4 › Level 154 › 154.4.a

Newspace 154.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(154))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
154.4.a.a	1	$\mathbb{Q}$	$q - 2q^{2} - 5q^{3} + 4q^{4} - q^{5} + 10q^{6} - 7q^{7} + O(q^{8})$	+ + +	$+1$
154.4.a.b	1	$\mathbb{Q}$	$q - 2q^{2} + 4q^{4} + 2q^{5} - 7q^{7} + O(q^{8})$	+ + −	$-1$
154.4.a.c	1	$\mathbb{Q}$	$q + 2q^{2} - 10q^{3} + 4q^{4} - 14q^{5} - 20q^{6} + 7q^{7} + O(q^{8})$	− − +	$+1$
154.4.a.d	1	$\mathbb{Q}$	$q + 2q^{2} - 2q^{3} + 4q^{4} + 18q^{5} - 4q^{6} + 7q^{7} + O(q^{8})$	− − +	$+1$
154.4.a.e	1	$\mathbb{Q}$	$q + 2q^{2} + 7q^{3} + 4q^{4} + 3q^{5} + 14q^{6} + 7q^{7} + O(q^{8})$	− − +	$+1$
154.4.a.f	2	$\mathbb{Q}(\sqrt{137})$	$2q - 4q^{2} - 5q^{3} + 8q^{4} - 7q^{5} + 10q^{6} + 14q^{7} + O(q^{8})$	+ − +	$-1$
154.4.a.g	2	$\mathbb{Q}(\sqrt{37})$	$2q - 4q^{2} + 6q^{3} + 8q^{4} + 26q^{5} - 12q^{6} + 14q^{7} + O(q^{8})$	+ − −	$+1$
154.4.a.h	2	$\mathbb{Q}(\sqrt{57})$	$2q + 4q^{2} - 5q^{3} + 8q^{4} - 17q^{5} - 10q^{6} - 14q^{7} + O(q^{8})$	− + +	$-1$
154.4.a.i	3	degree 3	$3q + 6q^{2} + 6q^{3} + 12q^{4} + 26q^{5} + 12q^{6} - 21q^{7} + O(q^{8})$	− + −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5} + 5T_{13} + 7T_{17} + 9T_{19}$ 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 $T$
154.4.a.a	$x - 592$
154.4.a.b	$x + 618$
154.4.a.c	$x - 1668$
154.4.a.d	$x - 332$
154.4.a.e	$x - 104$
154.4.a.f	$x^{2} + 826x + 98096$
154.4.a.g	$x^{2} + 144x - 1416208$
154.4.a.h	$x^{2} + 2172x + 867264$
154.4.a.i	$x^{3} - 404x^{2} - 1468728x - 477986832$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(154))$	14
Old forms	54
Cusp forms $S_{4}(\Gamma_0(154))$	68
Eisenstein series $E_{4}(\Gamma_0(154))$	8
Modular forms $M_{4}(\Gamma_0(154))$	76

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(154)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(7))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(11))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(14))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(22))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(77))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.213 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, 7, 11, 14, 22, 77, 154]: [1, 2, 3, 4, 8, 11, 26, 76] (certified at ell = 2147482951)
T = [(3, 1), (5, 3), (13, 5), (17, 7), (19, 9)]; h of degree 14 = 1 x 14 (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(154, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 154:4 1000

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