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

• Label: 315.8.u
• Level: $315$
• Weight: $8$
• Character orbit: 315.u
• Rep. character: $\chi_{315}(59,\cdot)$
• 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.u (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 - 20990 * q^4 - 6 * q^5 + 768 * q^6 + 1326 * q^9 - 6 * q^10 + 26826 * q^14 - 11226 * q^15 - 1310462 * q^16 - 12 * q^19 + 384 * q^20 - 37896 * q^21 - 280392 * q^24 - 2 * q^25 + 768 * q^26 + 288042 * q^29 + 781308 * q^30 - 6 * q^31 + 768 * q^34 + 86940 * q^35 - 1193004 * q^36 + 1235352 * q^39 - 711402 * q^41 + 2466048 * q^44 + 1292748 * q^45 + 300492 * q^46 + 650674 * q^49 + 1347546 * q^50 - 1949670 * q^51 + 5889948 * q^54 - 3755898 * q^56 - 6 * q^59 + 1929756 * q^60 + 3865440 * q^61 + 159317488 * q^64 + 7970022 * q^65 + 2932602 * q^66 - 7810044 * q^69 - 3338652 * q^70 - 9025368 * q^75 + 99840 * q^76 + 6354656 * q^79 - 11240895 * q^80 + 23049798 * q^81 + 38000250 * q^84 - 78127 * q^85 + 14485644 * q^89 + 37762167 * q^90 + 3294164 * q^91 - 6 * q^94 + 6559827 * q^95 + 27328506 * 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.