Atlas › Modular forms › Weight 2 › Level 567 › 567.2.a

Newspace 567.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(567))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
567.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - q^{4} + q^{5} - q^{7} + O(q^{8})$	+	567b1 rank 1
567.2.a.b	1	$\mathbb{Q}$	$q + q^{2} - q^{4} - q^{5} - q^{7} + O(q^{8})$	+	567a1 rank 1
567.2.a.c	3	degree 3	$3q - 3q^{2} + 3q^{4} - 3q^{5} + 3q^{7} + O(q^{8})$	−
567.2.a.d	3	degree 3	$3q - q^{2} + 3q^{4} - 5q^{5} - 3q^{7} + O(q^{8})$	+
567.2.a.e	3	degree 3	$3q + 6q^{4} - 3q^{5} + 3q^{7} + O(q^{8})$	−
567.2.a.f	3	degree 3	$3q + 6q^{4} + 3q^{5} + 3q^{7} + O(q^{8})$	−
567.2.a.g	3	degree 3	$3q + q^{2} + 3q^{4} + 5q^{5} - 3q^{7} + O(q^{8})$	+
567.2.a.h	3	degree 3	$3q + 3q^{2} + 3q^{4} + 3q^{5} + 3q^{7} + O(q^{8})$	−
567.2.a.i	4	degree 4	$4q + 2q^{4} - 4q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{5}$ 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 $T$
567.2.a.a	$x - 2$
567.2.a.b	$x + 2$
567.2.a.c	$x^{3} + 12x^{2} + 27x - 3$
567.2.a.d	$x^{3} + 16x^{2} + 29x - 307$
567.2.a.e	$x^{3} + 9x^{2} - 69x - 138$
567.2.a.f	$x^{3} - 9x^{2} - 69x + 138$
567.2.a.g	$x^{3} - 16x^{2} + 29x + 307$
567.2.a.h	$x^{3} - 12x^{2} + 27x + 3$
567.2.a.i	$x^{4} - 209x^{2} + 4489$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(567))$	24
Old forms	37
Cusp forms $S_{2}(\Gamma_0(567))$	61
Eisenstein series $E_{2}(\Gamma_0(567))$	23
Modular forms $M_{2}(\Gamma_0(567))$	84

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(567)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(21))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(27))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(63))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(81))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(189))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.237 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, 7, 9, 21, 27, 63, 81, 189, 567]: [0, 1, 1, 2, 4, 4, 10, 10, 26, 74] (certified at ell = 2147483179)
T = [(2, 1), (5, 3)]; h of degree 24 = 1 x 24 (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(567, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 567:2 1000

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