Space of modular forms of level 315, weight 8, and Character 315.k

• Label: 315.8.k
• Level: $315$
• Weight: $8$
• Character orbit: 315.k
• Rep. character: $\chi_{315}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $448$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(315, [\chi])\).

	Total	New	Old
Modular forms	680	448	232
Cusp forms	664	448	216
Eisenstein series	16	0	16

Trace form

448 * q - 14336 * q^4 - 1000 * q^5 - 928 * q^6 + 166 * q^7 - 180 * q^9 - 5908 * q^11 + 18460 * q^12 - 3694 * q^13 - 66924 * q^14 + 1750 * q^15 - 917504 * q^16 + 78608 * q^17 - 38316 * q^18 + 44684 * q^19 + 96000 * q^20 - 29824 * q^21 + 93756 * q^23 + 388108 * q^24 + 7000000 * q^25 - 52928 * q^26 + 125502 * q^27 + 42496 * q^28 + 46250 * q^29 - 52000 * q^30 + 215048 * q^31 - 1068460 * q^32 - 320212 * q^33 + 1998840 * q^36 + 12434 * q^37 - 2296136 * q^38 + 139892 * q^39 - 1023362 * q^41 + 2888388 * q^42 + 96104 * q^43 + 706306 * q^44 - 756750 * q^45 + 301008 * q^46 + 2767916 * q^47 - 9937012 * q^48 - 943334 * q^49 - 3009670 * q^51 + 1891328 * q^52 + 1704240 * q^53 + 11781120 * q^54 + 10177374 * q^56 + 574682 * q^57 + 405710 * q^59 + 1233750 * q^60 - 4157908 * q^61 - 26463048 * q^62 + 18271538 * q^63 + 117440512 * q^64 + 733250 * q^65 + 31041712 * q^66 + 2503718 * q^67 - 28063612 * q^68 + 25802760 * q^69 + 582000 * q^70 + 25622832 * q^71 + 17995544 * q^72 - 11731804 * q^73 - 21035536 * q^74 + 11439104 * q^76 - 2998790 * q^77 - 20513240 * q^78 + 215336 * q^79 + 14336000 * q^80 - 10015984 * q^81 + 32228716 * q^83 - 47107440 * q^84 + 1317750 * q^85 - 45089716 * q^86 + 6931826 * q^87 - 6662642 * q^89 + 3966750 * q^90 + 3448178 * q^91 - 34516540 * q^92 + 2684412 * q^93 - 11585184 * q^94 - 108079166 * q^96 + 6614834 * q^97 + 43594730 * q^98 + 9411390 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)