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

• Label: 315.10.bs
• Level: $315$
• Weight: $10$
• Character orbit: 315.bs
• Rep. character: $\chi_{315}(52,\cdot)$
• 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.bs (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 - 6 * q^3 - 6 * q^5 - 2 * q^7 + 2032 * q^8 - 12 * q^10 + 30828 * q^11 - 3078 * q^12 + 120868 * q^15 - 109051912 * q^16 + 1578660 * q^17 - 272258 * q^18 + 3145728 * q^20 + 630624 * q^21 - 2052 * q^22 - 2811846 * q^23 + 2 * q^25 - 24 * q^26 + 3339324 * q^27 + 525304 * q^28 + 13436806 * q^30 + 33565140 * q^32 - 6 * q^33 - 5171624 * q^35 + 54695920 * q^36 - 4 * q^37 - 6 * q^38 - 6 * q^40 - 6695412 * q^41 + 16305200 * q^42 - 4 * q^43 + 188547786 * q^45 - 12858056 * q^46 + 1457838 * q^48 - 399994588 * q^50 + 113515220 * q^51 + 3145722 * q^52 + 192599116 * q^53 - 230302348 * q^56 - 280253572 * q^57 - 102971198 * q^58 - 181652734 * q^60 + 870864924 * q^63 + 884603468 * q^65 - 12 * q^66 - 4 * q^67 - 1616553990 * q^68 + 7812498 * q^70 - 765444160 * q^71 + 58576486 * q^72 - 12 * q^73 - 1320274854 * q^75 + 3145728 * q^76 + 1533549434 * q^77 - 2268723542 * q^78 + 1572852 * q^80 - 1372979644 * q^81 - 3084 * q^82 + 288011976 * q^83 - 4 * q^85 - 1692494632 * q^86 - 1570486578 * q^87 + 269486082 * q^88 - 4056652224 * q^90 - 16 * q^91 - 2158449668 * q^92 + 108737758 * q^93 - 2236489820 * q^95 - 9370888800 * q^96 - 7862348820 * 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.