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

• Label: 315.10.z
• Level: $315$
• Weight: $10$
• Character orbit: 315.z
• Rep. character: $\chi_{315}(104,\cdot)$
• 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.z (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 - 108548 * q^4 + 35484 * q^9 - 46248 * q^11 + 191130 * q^14 + 134466 * q^15 - 27265028 * q^16 + 2594202 * q^21 - 2 * q^25 - 17450256 * q^29 - 8793624 * q^30 - 24103212 * q^36 - 117999072 * q^39 - 25712016 * q^46 + 31071544 * q^49 + 95246778 * q^50 - 192014508 * q^51 - 491387286 * q^56 + 421620336 * q^60 + 13423874032 * q^64 + 577042470 * q^65 + 316194 * q^70 + 6132 * q^74 - 902142472 * q^79 - 1970461308 * q^81 + 2576879214 * q^84 + 3906248 * q^85 - 2612159700 * q^86 + 161414420 * q^91 - 6709069824 * q^95 - 5213432844 * 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.