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Properties

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 $480$

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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

\( 856 q + 217084 q^{4} - 3 q^{5} - 3072 q^{6} + 32946 q^{9} + O(q^{10}) \) \( 856 q + 217084 q^{4} - 3 q^{5} - 3072 q^{6} + 32946 q^{9} - 6 q^{10} + 46230 q^{11} + 191130 q^{14} + 374829 q^{15} + 54523900 q^{16} - 12 q^{19} - 1536 q^{20} + 661794 q^{21} - 1690968 q^{24} + q^{25} - 3072 q^{26} + 8725110 q^{29} + 6598173 q^{30} - 3072 q^{34} - 21486285 q^{35} + 52186836 q^{36} - 41341416 q^{39} - 5862450 q^{40} - 3347706 q^{41} + 44196864 q^{44} - 94273899 q^{45} - 6431076 q^{46} + 31071544 q^{49} - 250352070 q^{50} - 75471282 q^{51} - 292817796 q^{54} - 95332272 q^{56} - 12 q^{59} + 168922605 q^{60} + 13420722160 q^{64} - 118104 q^{66} - 923126070 q^{69} + 121377015 q^{70} - 6150 q^{74} - 17824413 q^{75} - 1579008 q^{76} - 288112900 q^{79} - 129282729 q^{80} + 1964993586 q^{81} - 3798242178 q^{84} - 1953127 q^{85} + 3585717960 q^{86} - 3963797622 q^{89} - 653445327 q^{90} + 161414420 q^{91} + 3759202596 q^{96} + 1263230922 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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