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

• Label: 315.10.bz
• Level: $315$
• Weight: $10$
• Character orbit: 315.bz
• Rep. character: $\chi_{315}(73,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $712$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.bz (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
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	1760	728	1032
Cusp forms	1696	712	984
Eisenstein series	64	16	48

Trace form

712 * q + 2 * q^2 - 1698 * q^5 - 13572 * q^7 + 628 * q^8 - 153798 * q^10 - 26096 * q^11 + 22007172 * q^16 + 1578678 * q^17 - 2128008 * q^22 - 5311142 * q^23 - 1461706 * q^25 + 2294604 * q^26 - 20603030 * q^28 + 8900220 * q^31 - 16423146 * q^32 + 1952664 * q^35 - 12375026 * q^37 - 20958660 * q^38 - 89260962 * q^40 + 4009072 * q^43 + 2421124 * q^46 + 147698766 * q^47 - 350932780 * q^50 - 126665976 * q^52 - 208887686 * q^53 + 444503996 * q^56 + 130611606 * q^58 + 429110448 * q^61 - 50642882 * q^65 + 315475178 * q^67 + 408371100 * q^68 - 2051911728 * q^70 - 1175832080 * q^71 - 516971382 * q^73 - 264928990 * q^77 - 3775239504 * q^80 + 3707550078 * q^82 - 2869623792 * q^85 + 2815202248 * q^86 + 21295996 * q^88 + 2561145640 * q^91 + 11233897052 * q^92 - 279877586 * q^95 - 11494866 * 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.

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)