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

• Label: 315.10.d
• Level: $315$
• Weight: $10$
• Character orbit: 315.d
• Rep. character: $\chi_{315}(64,\cdot)$
• Character field: $\Q$
• Dimension: $134$
• Sturm bound: $480$

Defining parameters

Level:	$N$	$=$	$315 = 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	315.d (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Sturm bound:			$480$

Dimensions

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

	Total	New	Old
Modular forms	440	134	306
Cusp forms	424	134	290
Eisenstein series	16	0	16

Trace form

134 * q - 34476 * q^4 + 1470 * q^5 + 6472 * q^10 + 132540 * q^11 - 153664 * q^14 + 10587596 * q^16 - 1380456 * q^19 - 2867080 * q^20 + 8658890 * q^25 + 2413124 * q^26 - 7743544 * q^29 + 242424 * q^31 - 25026172 * q^34 - 3102092 * q^35 + 78114644 * q^40 + 60920844 * q^41 - 158503264 * q^44 - 100255568 * q^46 - 772483334 * q^49 - 198260556 * q^50 + 28643744 * q^55 + 74479020 * q^56 - 586643040 * q^59 - 443019628 * q^61 - 3040631340 * q^64 + 120220328 * q^65 - 80126172 * q^70 + 272448344 * q^71 + 162830520 * q^74 + 2046222848 * q^76 + 283274356 * q^79 + 1870645800 * q^80 - 1368964788 * q^85 - 51830696 * q^86 + 831757084 * q^89 - 978273044 * q^91 + 2698851508 * q^94 + 4090420484 * 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}}(5, [\chi])$$^{\oplus 6}$$\oplus$$S_{10}^{\mathrm{new}}(15, [\chi])$$^{\oplus 4}$$\oplus$$S_{10}^{\mathrm{new}}(35, [\chi])$$^{\oplus 3}$$\oplus$$S_{10}^{\mathrm{new}}(45, [\chi])$$^{\oplus 2}$$\oplus$$S_{10}^{\mathrm{new}}(105, [\chi])$$^{\oplus 2}$