Space of modular forms of level 315, weight 10, and Character 315.cb

• Label: 315.10.cb
• Level: $315$
• Weight: $10$
• Character orbit: 315.cb
• Rep. character: $\chi_{315}(13,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1712$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.cb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

	Total	New	Old
Modular forms	1744	1744	0
Cusp forms	1712	1712	0
Eisenstein series	32	32	0

Trace form

1712 * q - 4 * q^2 - 2 * q^7 - 4112 * q^8 + 30816 * q^11 - 241760 * q^15 + 54525944 * q^16 - 278408 * q^18 + 630624 * q^21 + 4092 * q^22 - 2811852 * q^23 - 4 * q^25 - 1050632 * q^28 + 43987264 * q^30 - 15209712 * q^32 + 1089712 * q^35 - 104181776 * q^36 - 16 * q^37 + 42969218 * q^42 - 4 * q^43 - 51432224 * q^46 - 169595356 * q^50 - 120043624 * q^51 + 770396464 * q^53 - 31641280 * q^56 + 279508328 * q^57 + 205942396 * q^58 - 194778640 * q^60 - 145573446 * q^63 - 442301740 * q^65 - 4 * q^67 + 7812498 * q^70 - 765444160 * q^71 + 1497030340 * q^72 - 503474614 * q^77 + 1420578196 * q^78 - 1173092488 * q^81 - 4 * q^85 + 3384989264 * q^86 - 538966020 * q^88 - 16 * q^91 - 2161598468 * q^92 - 1567710212 * q^93 - 2259927320 * q^95 + 2733457680 * q^98

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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