Atlas › Modular forms › Weight 2 › Level 195 › 195.2.a

Newspace 195.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(195))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
195.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + O(q^{8})$	− − −	$+1$	195a1 rank 0
195.2.a.b	1	$\mathbb{Q}$	$q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} + 3q^{7} + O(q^{8})$	+ − +	$+1$	195d1 rank 0
195.2.a.c	1	$\mathbb{Q}$	$q + 2q^{2} + q^{3} + 2q^{4} - q^{5} + 2q^{6} - q^{7} + O(q^{8})$	− + +	$+1$	195c1 rank 0
195.2.a.d	1	$\mathbb{Q}$	$q + 2q^{2} + q^{3} + 2q^{4} + q^{5} + 2q^{6} - 3q^{7} + O(q^{8})$	− − −	$+1$	195b1 rank 0
195.2.a.e	3	degree 3	$3q - 3q^{3} + 8q^{4} - 3q^{5} + q^{7} + O(q^{8})$	+ + −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{7} + 5T_{11} + 7T_{17} + 9T_{19}$ 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 $T$
195.2.a.a	$x + 3$
195.2.a.b	$x + 19$
195.2.a.c	$x + 79$
195.2.a.d	$x - 21$
195.2.a.e	$x^{3} - 55x^{2} - 5921x + 212263$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(195))$	7
Old forms	18
Cusp forms $S_{2}(\Gamma_0(195))$	25
Eisenstein series $E_{2}(\Gamma_0(195))$	7
Modular forms $M_{2}(\Gamma_0(195))$	32

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(195)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(15))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(39))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(65))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.106 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, 5, 13, 15, 39, 65, 195]: [0, 1, 1, 1, 4, 6, 8, 32] (certified at ell = 2147483629)
T = [(2, 1), (7, 3), (11, 5), (17, 7), (19, 9)]; h of degree 7 = 1 x 7 (phi(ord eps) x dim S_k^new); 2 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(195, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 195:2 1000

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