Atlas › Modular forms › Weight 2 › Level 587 › 587.2.a

Newspace 587.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(587))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
587.2.a.a	5	degree 5	$5q - 3q^{2} - 2q^{3} + 5q^{4} + 2q^{5} - 4q^{7} + O(q^{8})$	+	$-1$
587.2.a.b	13	degree 13	$13q - 3q^{2} - 2q^{3} + 5q^{4} - 11q^{5} - 8q^{6} - 15q^{7} + O(q^{8})$	+	$-1$
587.2.a.c	31	degree 31	$31q + 6q^{2} + 2q^{3} + 38q^{4} + 7q^{5} - 4q^{6} + 19q^{7} + O(q^{8})$	−	$+1$

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 $T$
587.2.a.a	$x^{5} + 5x^{4} - x^{3} - 7x^{2} + 2x + 1$
587.2.a.b	$x^{13} + 5x^{12} - 19x^{11} - 100x^{10} + 128x^{9} + 646x^{8} - 398x^{7} - 1551x^{6} + 761x^{5} + 1251x^{4} - 695x^{3} + 18x^{2} + 19x + 1$
587.2.a.c	$x^{31} - 8x^{30} - 78x^{29} + 747x^{28} + 2226x^{27} - 29097x^{26} - 24831x^{25} + 628767x^{24} - 73063x^{23} - 8443758x^{22} + 5227833x^{21} + 74892263x^{20} - 66394187x^{19} - 455561581x^{18} + 465908863x^{17} + 1944329198x^{16} - 2107023535x^{15} - 5891763932x^{14} + 6485639578x^{13} + 12705899910x^{12} - 13855675179x^{11} - 19358283998x^{10} + 20501622315x^{9} + 20443566763x^{8} - 20536815541x^{7} - 14443941272x^{6} + 13222192173x^{5} + 6418161242x^{4} - 4903545446x^{3} - 1602180139x^{2} + 788541831x + 173143604$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(587))$	49
Old forms	0
Cusp forms $S_{2}(\Gamma_0(587))$	49
Eisenstein series $E_{2}(\Gamma_0(587))$	1
Modular forms $M_{2}(\Gamma_0(587))$	50

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.206 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, 587]: [0, 50] (certified at ell = 2147470837)
T = [(2, 1), (3, 1)]; h of degree 49 = 1 x 49 (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(587, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 587:2 1000

← 586.2.a · 588.2.a →