Space of modular forms of level 325, weight 10, and Character 325.x

• Label: 325.10.x
• Level: $325$
• Weight: $10$
• Character orbit: 325.x
• Rep. character: $\chi_{325}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $748$
• Sturm bound: $350$

Defining parameters

Level:	$N$	$=$	$325 = 5^{2} \cdot 13$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	325.x (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$65$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$350$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(325, [\chi])$.

	Total	New	Old
Modular forms	1284	764	520
Cusp forms	1236	748	488
Eisenstein series	48	16	32

Trace form

748 * q + 6 * q^2 + 2 * q^3 + 94720 * q^4 - 8 * q^6 + 2 * q^7 - 10176 * q^9 - 175504 * q^11 - 229936 * q^12 - 107516 * q^13 - 23724036 * q^16 - 475324 * q^17 - 2728900 * q^18 + 690200 * q^19 - 892024 * q^21 + 1658284 * q^22 + 2148070 * q^23 - 6308872 * q^24 - 13748520 * q^26 + 2304956 * q^27 - 1049598 * q^28 + 8552728 * q^31 - 40064088 * q^32 + 39880482 * q^33 + 42481792 * q^34 - 10420236 * q^36 + 5487064 * q^37 + 2048 * q^38 - 29153152 * q^39 + 2905558 * q^41 + 142596440 * q^42 + 92584150 * q^43 + 196675536 * q^44 - 218048904 * q^46 - 32812760 * q^47 + 211055716 * q^48 - 1842013622 * q^49 - 31064050 * q^52 + 39224590 * q^53 + 98329416 * q^54 + 300711924 * q^56 - 392252870 * q^58 - 728627032 * q^59 - 144278948 * q^61 + 46102604 * q^62 + 1864917756 * q^63 - 11609837568 * q^64 + 212935152 * q^66 + 86495142 * q^67 - 1144029472 * q^68 - 145376352 * q^69 + 665628056 * q^71 - 1306439794 * q^72 - 1499347584 * q^74 + 1625883544 * q^76 - 547625732 * q^77 - 5804427948 * q^78 + 15681672242 * q^81 + 1993727534 * q^82 + 3934978272 * q^83 + 7169897848 * q^84 + 3676106208 * q^86 + 4448862214 * q^87 - 7081956642 * q^88 - 112242 * q^89 - 4868202656 * q^91 + 2958520328 * q^92 - 429096692 * q^93 - 5112943872 * q^94 + 10843988360 * q^96 - 339114846 * q^97 - 4377520950 * q^98 + 8199810172 * q^99

Decomposition of $S_{10}^{\mathrm{new}}(325, [\chi])$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of $S_{10}^{\mathrm{old}}(325, [\chi])$ into lower level spaces

$S_{10}^{\mathrm{old}}(325, [\chi]) \simeq$ $S_{10}^{\mathrm{new}}(65, [\chi])$$^{\oplus 2}$