Space of modular forms of level 315, weight 10, and Character 315.bf

• Label: 315.10.bf
• Level: $315$
• Weight: $10$
• Character orbit: 315.bf
• Rep. character: $\chi_{315}(109,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $356$
• Sturm bound: $480$

Defining parameters

Level:	$N$	$=$	$315 = 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$35$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$480$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(315, [\chi])$.

	Total	New	Old
Modular forms	880	364	516
Cusp forms	848	356	492
Eisenstein series	32	8	24

Trace form

356 * q + 45054 * q^4 + 285 * q^5 + 15700 * q^10 + 51408 * q^11 + 502462 * q^14 - 11002566 * q^16 + 1081088 * q^19 - 662336 * q^20 + 3480701 * q^25 + 10213594 * q^26 + 10674676 * q^29 - 12099478 * q^31 + 11333024 * q^34 - 4603189 * q^35 + 33143438 * q^40 - 62636976 * q^41 - 103230182 * q^44 + 101875494 * q^46 - 157542714 * q^49 + 455089284 * q^50 + 127740898 * q^55 + 94310784 * q^56 - 394583406 * q^59 - 143715852 * q^61 - 5432943260 * q^64 + 339019282 * q^65 + 31554150 * q^70 - 835013312 * q^71 + 497689842 * q^74 + 153484300 * q^76 - 440796746 * q^79 + 361564056 * q^80 - 2722868530 * q^85 + 537431948 * q^86 - 1162710640 * q^89 - 210659788 * q^91 - 64378086 * q^94 - 602198285 * q^95

Decomposition of $S_{10}^{\mathrm{new}}(315, [\chi])$ into newform subspaces

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

Decomposition of $S_{10}^{\mathrm{old}}(315, [\chi])$ into lower level spaces

$S_{10}^{\mathrm{old}}(315, [\chi]) \simeq$ $S_{10}^{\mathrm{new}}(35, [\chi])$$^{\oplus 3}$$\oplus$$S_{10}^{\mathrm{new}}(105, [\chi])$$^{\oplus 2}$