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

• Label: 315.10.bq
• Level: $315$
• Weight: $10$
• Character orbit: 315.bq
• Rep. character: $\chi_{315}(164,\cdot)$
• 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.bq (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 + 217084 * q^4 - 3 * q^5 - 3072 * q^6 + 32946 * q^9 - 6 * q^10 + 46230 * q^11 + 191130 * q^14 + 374829 * q^15 + 54523900 * q^16 - 12 * q^19 - 1536 * q^20 + 661794 * q^21 - 1690968 * q^24 + q^25 - 3072 * q^26 + 8725110 * q^29 + 6598173 * q^30 - 3072 * q^34 - 21486285 * q^35 + 52186836 * q^36 - 41341416 * q^39 - 5862450 * q^40 - 3347706 * q^41 + 44196864 * q^44 - 94273899 * q^45 - 6431076 * q^46 + 31071544 * q^49 - 250352070 * q^50 - 75471282 * q^51 - 292817796 * q^54 - 95332272 * q^56 - 12 * q^59 + 168922605 * q^60 + 13420722160 * q^64 - 118104 * q^66 - 923126070 * q^69 + 121377015 * q^70 - 6150 * q^74 - 17824413 * q^75 - 1579008 * q^76 - 288112900 * q^79 - 129282729 * q^80 + 1964993586 * q^81 - 3798242178 * q^84 - 1953127 * q^85 + 3585717960 * q^86 - 3963797622 * q^89 - 653445327 * q^90 + 161414420 * q^91 + 3759202596 * 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.