Atlas › Modular forms › Weight 10 › Level 25 › 25.10.a

Newspace 25.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(25))$

Newforms

Label	Dim	Coefficient field	Trace form
25.10.a.a	1	$\mathbb{Q}$	$q + 8q^{2} + 114q^{3} - 448q^{4} + 912q^{6} - 4242q^{7} + O(q^{8})$
25.10.a.b	2	$\mathbb{Q}(\sqrt{1009})$	$2q + 10q^{2} - 260q^{3} + 1044q^{4} - 5336q^{6} - 1700q^{7} + O(q^{8})$
25.10.a.c	3	degree 3	$3q - 33q^{2} - 89q^{3} + 341q^{4} + 3421q^{6} - 5258q^{7} + O(q^{8})$
25.10.a.d	3	degree 3	$3q + 33q^{2} + 89q^{3} + 341q^{4} + 3421q^{6} + 5258q^{7} + O(q^{8})$
25.10.a.e	4	degree 4	$4q + 1368q^{4} + 2808q^{6} + O(q^{8})$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
25.10.a.a	$x - 122$
25.10.a.b	$x^{2} + 250x + 14616$
25.10.a.c	$x^{3} + 122x^{2} - 55559x - 584448$
25.10.a.d	$x^{3} - 122x^{2} - 55559x + 584448$
25.10.a.e	$x^{4} - 38068x^{2} + 198470656$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(25))$	13
Old forms	6
Cusp forms $S_{10}(\Gamma_0(25))$	19
Eisenstein series $E_{10}(\Gamma_0(25))$	6
Modular forms $M_{10}(\Gamma_0(25))$	25

Decomposition of the old subspace

$S_{10}^{\mathrm{old}}(\Gamma_0(25)) =$ $S_{10}^{\mathrm{new}}(\Gamma_0(5))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.304 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, 5, 25]: [1, 5, 23] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 13 = 1 x 13 (phi(ord eps) x dim S_k^new); 4 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(25, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 25:10 1000

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