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Properties

Label 315.6.bh
Level $315$
Weight $6$
Character orbit 315.bh
Rep. character $\chi_{315}(169,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $360$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 315.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(315, [\chi])\).

Total New Old
Modular forms 488 360 128
Cusp forms 472 360 112
Eisenstein series 16 0 16

Trace form

\( 360 q + 2880 q^{4} + 58 q^{5} - 344 q^{9} + O(q^{10}) \) \( 360 q + 2880 q^{4} + 58 q^{5} - 344 q^{9} + 1746 q^{11} - 1568 q^{14} - 260 q^{15} - 46080 q^{16} - 2886 q^{20} + 490 q^{21} + 24852 q^{24} + 3306 q^{25} - 1760 q^{26} - 18764 q^{29} - 20020 q^{30} + 8868 q^{31} + 12660 q^{34} - 12972 q^{36} + 18202 q^{39} + 5240 q^{41} + 271040 q^{44} + 143838 q^{45} - 53880 q^{46} + 432180 q^{49} + 23230 q^{50} + 58490 q^{51} - 149964 q^{54} + 27588 q^{55} + 75264 q^{56} + 26684 q^{59} - 144528 q^{60} - 1366680 q^{64} + 119620 q^{65} + 22840 q^{66} + 446260 q^{69} - 614472 q^{71} - 27292 q^{74} + 231900 q^{75} + 50340 q^{76} - 36030 q^{79} - 1021576 q^{80} + 400712 q^{81} + 62720 q^{84} - 81624 q^{85} + 79940 q^{86} + 571600 q^{89} + 401924 q^{90} + 32340 q^{91} - 115728 q^{94} + 122180 q^{95} + 29052 q^{96} - 1277136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)