Atlas › Modular forms › Weight 10 › Level 27 › 27.10.a

Newspace 27.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(27))$

Newforms

Label	Dim	Coefficient field	Trace form
27.10.a.a	2	$\mathbb{Q}(\sqrt{14})$	$2q - 16q^{4} - 1526q^{7} + O(q^{8})$
27.10.a.b	3	degree 3	$3q - 3q^{2} + 597q^{4} + 1983q^{5} - 3693q^{7} + O(q^{8})$
27.10.a.c	3	degree 3	$3q + 3q^{2} + 597q^{4} - 1983q^{5} - 3693q^{7} + O(q^{8})$
27.10.a.d	4	degree 4	$4q + 2236q^{4} + 11852q^{7} + O(q^{8})$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{5}$ 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 $T$
27.10.a.a	$x^{2} - 222264$
27.10.a.b	$x^{3} - 1980x^{2} - 2018439x + 3869606358$
27.10.a.c	$x^{3} + 1980x^{2} - 2018439x - 3869606358$
27.10.a.d	$x^{4} - 5143662x^{2} + 4182260636160$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(27))$	12
Old forms	12
Cusp forms $S_{10}(\Gamma_0(27))$	24
Eisenstein series $E_{10}(\Gamma_0(27))$	6
Modular forms $M_{10}(\Gamma_0(27))$	30

Decomposition of the old subspace

$S_{10}^{\mathrm{old}}(\Gamma_0(27)) =$ $S_{10}^{\mathrm{new}}(\Gamma_0(3))^{\oplus 3}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(9))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.323 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, 3, 9, 27]: [1, 4, 10, 28] (certified at ell = 2147483647)
T = [(2, 1), (5, 1)]; h of degree 12 = 1 x 12 (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(27, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 27:10 1000

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