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

• Label: 315.8.bq
• Level: $315$
• Weight: $8$
• Character orbit: 315.bq
• Rep. character: $\chi_{315}(164,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $664$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.bq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(384\)

Dimensions

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

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

Trace form

664 * q + 41980 * q^4 - 3 * q^5 - 768 * q^6 - 936 * q^9 - 6 * q^10 - 8868 * q^11 + 26826 * q^14 - 11226 * q^15 + 2620924 * q^16 - 12 * q^19 - 384 * q^20 - 19500 * q^21 - 111432 * q^24 + q^25 - 768 * q^26 + 288042 * q^29 - 41043 * q^30 - 768 * q^34 - 86940 * q^35 - 1193004 * q^36 - 1330068 * q^39 - 235146 * q^40 + 711402 * q^41 - 2466048 * q^44 + 1194501 * q^45 + 300492 * q^46 - 325340 * q^49 + 1347546 * q^50 + 4164192 * q^51 + 5889180 * q^54 + 209712 * q^56 - 12 * q^59 - 643731 * q^60 + 159317488 * q^64 - 13128 * q^66 + 7810044 * q^69 - 399657 * q^70 - 1542 * q^74 - 16415076 * q^75 - 99840 * q^76 - 12709312 * q^79 + 11240895 * q^80 - 3256740 * q^81 + 3865758 * q^84 - 78127 * q^85 + 47153112 * q^86 - 14485644 * q^89 - 37762167 * q^90 + 3294164 * q^91 - 31994988 * q^96 - 278322 * 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.