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

• Label: 315.8.cb
• Level: $315$
• Weight: $8$
• Character orbit: 315.cb
• Rep. character: $\chi_{315}(13,\cdot)$
• 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.cb (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 - 4 * q^2 - 2 * q^7 - 1040 * q^8 - 5916 * q^11 + 25180 * q^15 + 2621432 * q^16 + 50104 * q^18 + 27888 * q^21 + 1020 * q^22 + 2292 * q^23 - 4 * q^25 - 66056 * q^28 - 1952096 * q^30 + 272496 * q^32 - 2540168 * q^35 + 733168 * q^36 - 16 * q^37 - 1613518 * q^42 - 4 * q^43 + 2408032 * q^46 - 3652636 * q^50 - 1146700 * q^51 + 725824 * q^53 - 2775328 * q^56 + 2523776 * q^57 - 1385540 * q^58 + 9734000 * q^60 - 4594944 * q^63 + 6322340 * q^65 - 4 * q^67 + 312498 * q^70 + 12089024 * q^71 + 8709028 * q^72 + 5925050 * q^77 - 33005612 * q^78 + 30557168 * q^81 - 4 * q^85 + 22333328 * q^86 - 8519172 * q^88 - 16 * q^91 + 309244 * q^92 + 15767128 * q^93 + 60086920 * q^95 - 132367152 * 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.