Atlas › Modular forms › Weight 4 › Level 106 › 106.4.a

Newspace 106.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(106))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
106.4.a.a	2	$\mathbb{Q}(\sqrt{3})$	$2q + 4q^{2} - 8q^{3} + 8q^{4} - 16q^{5} - 16q^{6} - 28q^{7} + O(q^{8})$	− +	$-1$
106.4.a.b	3	degree 3	$3q - 6q^{2} - 5q^{3} + 12q^{4} - 6q^{5} + 10q^{6} + 8q^{7} + O(q^{8})$	+ −	$-1$
106.4.a.c	3	degree 3	$3q - 6q^{2} + 4q^{3} + 12q^{4} + 19q^{5} - 8q^{6} - 6q^{7} + O(q^{8})$	+ +	$+1$
106.4.a.d	5	degree 5	$5q + 10q^{2} + q^{3} + 20q^{4} + 29q^{5} + 2q^{6} + 14q^{7} + O(q^{8})$	− −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
106.4.a.a	$x^{2} + 24x + 141$
106.4.a.b	$x^{3} + 11x^{2} + 11x - 77$
106.4.a.c	$x^{3} - 23x^{2} - 323x + 5641$
106.4.a.d	$x^{5} - 30x^{4} + 118x^{3} + 1346x^{2} - 10221x + 18398$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(106))$	13
Old forms	26
Cusp forms $S_{4}(\Gamma_0(106))$	39
Eisenstein series $E_{4}(\Gamma_0(106))$	4
Modular forms $M_{4}(\Gamma_0(106))$	43

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(106)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(53))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.109 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, 53, 106]: [1, 2, 15, 43] (certified at ell = 2147483053)
T = [(3, 1), (5, 1)]; h of degree 13 = 1 x 13 (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(106, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 106:4 1000

← 105.4.a · 107.4.a →