Atlas › Modular forms › Weight 6 › Level 108 › 108.6.a

Newspace 108.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(108))$

Newforms

Label	Dim	Coefficient field	Trace form	CM
108.6.a.a	1	$\mathbb{Q}$	$q - 25q^{7} + O(q^{8})$	$\mathbb{Q}(\sqrt{-3})$
108.6.a.b	2	$\mathbb{Q}(\sqrt{41})$	$2q - 32q^{7} + O(q^{8})$
108.6.a.c	2	$\mathbb{Q}(\sqrt{41})$	$2q - 32q^{7} + O(q^{8})$
108.6.a.d	2	$\mathbb{Q}(\sqrt{6})$	$2q + 58q^{7} + O(q^{8})$

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + T_{7}$ 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 $T$
108.6.a.a	$x + 25$
108.6.a.b	$x^{2} + 32x - 13028$
108.6.a.c	$x^{2} + 32x - 52880$
108.6.a.d	$x^{2} - 58x - 6935$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(108))$	7
Old forms	74
Cusp forms $S_{6}(\Gamma_0(108))$	81
Eisenstein series $E_{6}(\Gamma_0(108))$	18
Modular forms $M_{6}(\Gamma_0(108))$	99

Decomposition of the old subspace

$S_{6}^{\mathrm{old}}(\Gamma_0(108)) =$ $S_{6}^{\mathrm{new}}(\Gamma_0(3))^{\oplus 9}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(4))^{\oplus 4}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(6))^{\oplus 6}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(9))^{\oplus 6}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(18))^{\oplus 4}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(27))^{\oplus 3}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(36))^{\oplus 2}$ $\oplus$ $S_{6}^{\mathrm{new}}(\Gamma_0(54))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.308 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, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108]: [1, 2, 3, 4, 7, 6, 13, 17, 16, 33, 47, 93] (certified at ell = 2147483647)
T = [(5, 1), (7, 1)]; h of degree 7 = 1 x 7 (phi(ord eps) x dim S_k^new); 2 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(108, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 108:6 1000

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