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

• Label: 315.10.u
• Level: $315$
• Weight: $10$
• Character orbit: 315.u
• Rep. character: $\chi_{315}(59,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $856$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

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

	Total	New	Old
Modular forms	872	872	0
Cusp forms	856	856	0
Eisenstein series	16	16	0

Trace form

856 * q - 108542 * q^4 - 6 * q^5 + 3072 * q^6 - 17748 * q^9 - 6 * q^10 + 191130 * q^14 + 374829 * q^15 - 27261950 * q^16 - 12 * q^19 + 1536 * q^20 - 883182 * q^21 + 5116584 * q^24 - 2 * q^25 + 3072 * q^26 + 8725110 * q^29 - 22494108 * q^30 - 6 * q^31 + 3072 * q^34 + 21486285 * q^35 + 52186836 * q^36 + 31542534 * q^39 + 3347706 * q^41 - 44196864 * q^44 + 46107753 * q^45 - 6431076 * q^46 - 62143094 * q^49 - 250352070 * q^50 + 5974542 * q^51 - 292814724 * q^54 - 139645386 * q^56 - 6 * q^59 - 158018316 * q^60 + 36683436 * q^61 + 13420722160 * q^64 - 706657671 * q^65 + 1158645498 * q^66 + 923126070 * q^69 - 11401020 * q^70 + 152433687 * q^75 + 1579008 * q^76 + 144056450 * q^79 + 129282729 * q^80 - 779868744 * q^81 - 1092299718 * q^84 - 1953127 * q^85 + 3963797622 * q^89 + 653445327 * q^90 + 161414420 * q^91 - 6 * q^94 - 3903977973 * q^95 - 3932160006 * q^96 + 1263230922 * q^99

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

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