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Properties

Label 315.4.bq
Level $315$
Weight $4$
Character orbit 315.bq
Rep. character $\chi_{315}(164,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 315.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280 q + 1084 q^{4} - 3 q^{5} - 48 q^{6} + 42 q^{9} + O(q^{10}) \) \( 280 q + 1084 q^{4} - 3 q^{5} - 48 q^{6} + 42 q^{9} - 6 q^{10} + 6 q^{11} - 138 q^{14} + 69 q^{15} + 4060 q^{16} - 12 q^{19} - 24 q^{20} + 42 q^{21} - 552 q^{24} + q^{25} - 48 q^{26} + 114 q^{29} + 57 q^{30} - 48 q^{34} - 765 q^{35} + 660 q^{36} + 1128 q^{39} - 426 q^{40} + 618 q^{41} - 624 q^{44} - 699 q^{45} + 216 q^{46} + 196 q^{49} + 786 q^{50} - 1314 q^{51} + 2172 q^{54} - 3696 q^{56} - 12 q^{59} - 411 q^{60} + 14032 q^{64} - 168 q^{66} - 1686 q^{69} + 963 q^{70} - 102 q^{74} + 3579 q^{75} - 480 q^{76} - 1444 q^{79} + 3855 q^{80} - 390 q^{81} - 3426 q^{84} - 127 q^{85} - 12504 q^{86} + 1854 q^{89} - 507 q^{90} + 1364 q^{91} - 1356 q^{96} - 3606 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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