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

• Label: 315.10.cg
• Level: $315$
• Weight: $10$
• Character orbit: 315.cg
• Rep. character: $\chi_{315}(157,\cdot)$
• 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.cg (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 + 2 * q^2 - 6 * q^3 - 2 * q^7 + 2032 * q^8 - 12 * q^10 - 61656 * q^11 - 6 * q^12 + 120868 * q^15 + 54525956 * q^16 + 1578660 * q^17 + 550654 * q^18 - 3145728 * q^20 + 3484380 * q^21 - 2052 * q^22 + 5623692 * q^23 - 4 * q^25 - 24 * q^26 - 3339324 * q^27 + 525304 * q^28 - 8041904 * q^30 - 12 * q^31 - 16782570 * q^32 + 25279674 * q^33 - 5171624 * q^35 + 54695920 * q^36 - 4 * q^37 + 6695412 * q^41 + 16426370 * q^42 - 4 * q^43 - 92215518 * q^45 - 12858056 * q^46 - 6 * q^47 - 1457838 * q^48 - 399994588 * q^50 + 6528380 * q^51 + 192599116 * q^53 + 261943616 * q^56 - 280253572 * q^57 + 205942396 * q^58 + 495790850 * q^60 - 73366896 * q^61 + 392881734 * q^63 - 442301734 * q^65 - 120932364 * q^66 + 2 * q^67 - 15625002 * q^70 - 765444160 * q^71 + 55008970 * q^72 - 12 * q^73 - 6 * q^75 - 3145728 * q^76 - 1030074826 * q^77 - 2268723542 * q^78 + 1572852 * q^80 + 586546232 * q^81 - 3084 * q^82 - 288011976 * q^83 - 4 * q^85 + 3384989264 * q^86 - 118104 * q^87 - 538972164 * q^88 + 4056652224 * q^90 - 16 * q^91 - 2158449668 * q^92 + 712902418 * q^93 + 1118244910 * q^95 - 6253707276 * 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.