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

• Label: 315.8.r
• Level: $315$
• Weight: $8$
• Character orbit: 315.r
• Rep. character: $\chi_{315}(184,\cdot)$
• 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.r (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 - 41988 * q^4 + q^5 + 1176 * q^6 + 2080 * q^9 + 254 * q^10 - 2952 * q^11 - 7922 * q^14 + 15592 * q^15 + 2621948 * q^16 - 4 * q^19 - 32898 * q^20 - 63176 * q^21 - 205548 * q^24 + q^25 + 421564 * q^26 + 46246 * q^29 - 81439 * q^30 - 4 * q^31 - 260 * q^34 + 240684 * q^35 - 1486380 * q^36 + 676096 * q^39 - 110636 * q^40 + 2442602 * q^41 + 690428 * q^44 + 529227 * q^45 - 300500 * q^46 + 325336 * q^49 + 73258 * q^50 + 1676756 * q^51 + 1468680 * q^54 + 1021074 * q^55 + 2443272 * q^56 + 19716380 * q^59 - 5665359 * q^60 - 2576968 * q^61 - 159448592 * q^64 + 5000848 * q^65 + 9207448 * q^66 - 1758656 * q^69 - 3693573 * q^70 - 7650276 * q^71 + 10080038 * q^74 + 10042494 * q^75 + 33276 * q^76 + 12709304 * q^79 + 7818041 * q^80 - 13417684 * q^81 + 40137794 * q^84 - 78127 * q^85 - 35922268 * q^86 - 51992348 * q^89 - 32430127 * q^90 - 3294180 * q^91 + 23172412 * q^94 + 52248746 * q^95 + 64477020 * q^96 + 32138610 * 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.