Atlas › Modular forms › Weight 6 › Level 46 › 46.6.a

Newspace 46.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(46))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
46.6.a.a	2	$\mathbb{Q}(\sqrt{55})$	$2q - 8q^{2} + 6q^{3} + 32q^{4} - 68q^{5} - 24q^{6} + 96q^{7} + O(q^{8})$	+ +	$-1$
46.6.a.b	2	$\mathbb{Q}(\sqrt{2})$	$2q + 8q^{2} - 22q^{3} + 32q^{4} - 68q^{5} - 88q^{6} - 312q^{7} + O(q^{8})$	− −	$-1$
46.6.a.c	3	degree 3	$3q - 12q^{2} + 6q^{3} + 48q^{4} + 32q^{5} - 24q^{6} - 192q^{7} + O(q^{8})$	+ −	$+1$
46.6.a.d	3	degree 3	$3q + 12q^{2} + 14q^{3} + 48q^{4} + 82q^{5} + 56q^{6} + 172q^{7} + O(q^{8})$	− +	$+1$

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 $T$
46.6.a.a	$x^{2} + 62x - 2559$
46.6.a.b	$x^{2} + 90x - 1847$
46.6.a.c	$x^{3} - 38x^{2} - 7103x + 35928$
46.6.a.d	$x^{3} - 96x^{2} + 365x - 78$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(46))$	10
Old forms	18
Cusp forms $S_{6}(\Gamma_0(46))$	28
Eisenstein series $E_{6}(\Gamma_0(46))$	4
Modular forms $M_{6}(\Gamma_0(46))$	32

Decomposition of the old subspace

$S_{6}^{\mathrm{old}}(\Gamma_0(46)) =$ $S_{6}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.234 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, 23, 46]: [1, 2, 11, 32] (certified at ell = 2147483647)
T = [(3, 1), (5, 1)]; h of degree 10 = 1 x 10 (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(46, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 46:6 1000

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