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

• Label: 315.10.cc
• Level: $315$
• Weight: $10$
• Character orbit: 315.cc
• Rep. character: $\chi_{315}(92,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1296$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.cc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
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	1296	448
Cusp forms	1712	1296	416
Eisenstein series	32	0	32

Trace form

1296 * q - 296 * q^3 + 92472 * q^11 + 303104 * q^12 + 161296 * q^15 + 42467328 * q^16 - 2601544 * q^18 - 9781248 * q^20 - 38416 * q^21 - 8435544 * q^23 - 2922912 * q^25 + 1405408 * q^27 - 11065820 * q^30 + 48787140 * q^32 + 46238504 * q^33 - 49811104 * q^36 - 39658464 * q^37 - 23637888 * q^38 - 73794048 * q^41 - 60601240 * q^42 + 128777440 * q^45 - 41874192 * q^46 + 356541672 * q^47 - 72447976 * q^48 - 343310584 * q^51 - 107523504 * q^55 - 180725944 * q^57 - 1017411092 * q^60 - 255831352 * q^63 + 1326905208 * q^65 + 1312694080 * q^66 + 156313368 * q^67 - 1683178264 * q^72 + 3155754552 * q^75 - 333266616 * q^76 + 5952364152 * q^78 + 448912448 * q^81 - 2374534656 * q^82 - 5986843080 * q^83 + 992974032 * q^85 - 10317793536 * q^86 - 998690464 * q^87 - 2556977328 * q^88 + 11625991692 * q^90 - 1718693424 * q^91 - 3884263404 * q^92 - 7784586824 * q^93 - 9732599880 * q^95 - 12081775584 * q^96 + 5878265040 * q^97

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

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)