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

• Label: 315.10.be
• Level: $315$
• Weight: $10$
• Character orbit: 315.be
• Rep. character: $\chi_{315}(236,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $576$
• Sturm bound: $480$

Defining parameters

Level:	$N$	$=$	$315 = 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	315.be (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$63$
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	872	576	296
Cusp forms	856	576	280
Eisenstein series	16	0	16

Trace form

576 * q + 73728 * q^4 - 684 * q^7 - 17746 * q^9 - 194616 * q^13 + 191136 * q^14 - 132500 * q^15 - 18874368 * q^16 + 1660204 * q^18 + 553590 * q^21 + 5234688 * q^24 + 225000000 * q^25 - 11022720 * q^26 + 2113812 * q^27 + 700416 * q^28 + 8725122 * q^29 + 4760000 * q^30 - 23426280 * q^31 - 31592472 * q^33 + 24202824 * q^36 + 6476904 * q^37 + 154348440 * q^38 + 31014552 * q^39 - 3347706 * q^41 - 124940736 * q^42 - 32070024 * q^43 + 70411206 * q^44 - 31061250 * q^45 + 6429024 * q^46 + 116058492 * q^47 + 84986880 * q^48 - 53538372 * q^49 - 201089604 * q^51 - 311011656 * q^53 + 386455752 * q^54 - 644453862 * q^56 - 265550064 * q^57 - 72955500 * q^59 - 82893750 * q^60 - 525203082 * q^61 - 119540392 * q^63 - 9663676416 * q^64 - 69240000 * q^65 - 581971200 * q^66 - 278498556 * q^67 + 2027249940 * q^68 + 156060000 * q^70 - 1296773128 * q^72 + 1498681872 * q^77 + 421489704 * q^78 - 83541384 * q^79 + 773480438 * q^81 + 3717875580 * q^83 - 6031617804 * q^84 + 255015000 * q^85 - 204061476 * q^87 + 2706876102 * q^89 + 2708403750 * q^90 - 1754700300 * q^91 - 3677250444 * q^92 + 123013536 * q^93 + 10901789862 * q^96 - 1356263568 * q^97 + 3167872038 * q^98 + 8901336316 * q^99

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}}(63, [\chi])$$^{\oplus 2}$