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

• Label: 315.8.z
• Level: $315$
• Weight: $8$
• Character orbit: 315.z
• Rep. character: $\chi_{315}(104,\cdot)$
• 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.z (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 - 20996 * q^4 - 2664 * q^9 + 8850 * q^11 + 26826 * q^14 + 1104 * q^15 - 1311236 * q^16 + 104502 * q^21 - 2 * q^25 - 576120 * q^29 + 397944 * q^30 - 225324 * q^36 + 3862686 * q^39 + 1205040 * q^46 - 325340 * q^49 - 8563686 * q^50 + 2179302 * q^51 - 11277606 * q^56 - 9236016 * q^60 + 159515632 * q^64 - 12510504 * q^65 - 2870286 * q^70 + 1524 * q^74 - 4501546 * q^79 - 25439544 * q^81 - 10443906 * q^84 + 156248 * q^85 - 91018356 * q^86 + 3294164 * q^91 - 14833608 * q^95 + 14799240 * 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.