Atlas › Modular forms › Weight 4 › Level 145 › 145.4.a

Newspace 145.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(145))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
145.4.a.a	1	$\mathbb{Q}$	$q + q^{2} - 8q^{3} - 7q^{4} - 5q^{5} - 8q^{6} - 14q^{7} + O(q^{8})$	+ +	$+1$
145.4.a.b	6	degree 6	$6q - 7q^{2} - 13q^{3} + 17q^{4} + 30q^{5} - 21q^{6} - 79q^{7} + O(q^{8})$	− +	$-1$
145.4.a.c	6	degree 6	$6q - q^{2} - q^{3} + 21q^{4} - 30q^{5} - 29q^{6} + 3q^{7} + O(q^{8})$	+ −	$-1$
145.4.a.d	7	degree 7	$7q + 6q^{2} + q^{3} + 52q^{4} - 35q^{5} + 3q^{6} + 17q^{7} + O(q^{8})$	+ +	$+1$
145.4.a.e	8	degree 8	$8q + 5q^{2} + 17q^{3} + 41q^{4} + 40q^{5} + 3q^{6} + 33q^{7} + O(q^{8})$	− −	$+1$

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 $T$
145.4.a.a	$x + 7$
145.4.a.b	$x^{6} + 20x^{5} + 67x^{4} - 427x^{3} - 2054x^{2} - 329x + 3896$
145.4.a.c	$x^{6} + 2x^{5} - 77x^{4} + 133x^{3} + 324x^{2} + 183x + 32$
145.4.a.d	$x^{7} - 7x^{6} - 186x^{5} + 1045x^{4} + 9357x^{3} - 30574x^{2} - 143948x + 154644$
145.4.a.e	$x^{8} - 22x^{7} + 33x^{6} + 1851x^{5} - 7462x^{4} - 50267x^{3} + 242434x^{2} + 442092x - 2296348$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(145))$	28
Old forms	16
Cusp forms $S_{4}(\Gamma_0(145))$	44
Eisenstein series $E_{4}(\Gamma_0(145))$	4
Modular forms $M_{4}(\Gamma_0(145))$	48

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(145)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(5))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(29))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.116 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, 29, 145]: [1, 3, 9, 48] (certified at ell = 2147483549)
T = [(2, 1), (3, 1)]; h of degree 28 = 1 x 28 (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(145, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 145:4 1000

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