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

• Label: 315.8.bv
• Level: $315$
• Weight: $8$
• Character orbit: 315.bv
• Rep. character: $\chi_{315}(23,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1328$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	1360	1360	0
Cusp forms	1328	1328	0
Eisenstein series	32	32	0

Trace form

1328 * q - 2 * q^3 - 6 * q^5 - 1872 * q^6 - 2 * q^7 - 4 * q^10 - 17736 * q^11 + 17750 * q^12 - 4 * q^13 + 12586 * q^15 - 5242888 * q^16 + 81666 * q^17 + 49598 * q^18 - 12 * q^20 - 27904 * q^21 + 508 * q^22 + 6882 * q^23 + 2 * q^25 + 193504 * q^27 + 32504 * q^28 - 446330 * q^30 - 8 * q^31 + 582590 * q^33 - 219664 * q^36 - 4 * q^37 - 1542 * q^38 + 65538 * q^40 - 1422828 * q^41 - 72400 * q^42 - 4 * q^43 + 2832502 * q^45 - 602024 * q^46 + 2267618 * q^48 + 6607476 * q^50 - 2875576 * q^51 + 66050 * q^52 + 312484 * q^55 - 10303500 * q^56 - 2619952 * q^57 + 691746 * q^58 + 6666682 * q^60 + 5153920 * q^61 - 7751002 * q^63 + 15595780 * q^66 - 4 * q^67 + 21103098 * q^68 + 312498 * q^70 + 9090134 * q^72 - 4 * q^73 - 10184154 * q^75 - 65544 * q^76 + 8007498 * q^77 - 14131506 * q^78 - 839196 * q^80 + 16674416 * q^81 - 260 * q^82 - 12 * q^83 - 4 * q^85 + 29243472 * q^86 - 22103620 * q^87 - 4129278 * q^88 - 37869324 * q^90 - 16 * q^91 - 1321740 * q^92 + 26438026 * q^93 + 97411968 * q^96 - 4 * q^97 - 768 * q^98

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

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