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Properties

Label 315.10.be
Level $315$
Weight $10$
Character orbit 315.be
Rep. character $\chi_{315}(236,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 872 576 296
Cusp forms 856 576 280
Eisenstein series 16 0 16

Trace form

\( 576 q + 73728 q^{4} - 684 q^{7} - 17746 q^{9} - 194616 q^{13} + 191136 q^{14} - 132500 q^{15} - 18874368 q^{16} + 1660204 q^{18} + 553590 q^{21} + 5234688 q^{24} + 225000000 q^{25} - 11022720 q^{26} + 2113812 q^{27}+ \cdots + 8901336316 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)