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Properties

Label 315.5.bi
Level $315$
Weight $5$
Character orbit 315.bi
Rep. character $\chi_{315}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $156$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 315.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(315, [\chi])\).

Total New Old
Modular forms 400 164 236
Cusp forms 368 156 212
Eisenstein series 32 8 24

Trace form

\( 156 q + 606 q^{4} - 24 q^{5} + O(q^{10}) \) \( 156 q + 606 q^{4} - 24 q^{5} + 198 q^{10} - 118 q^{11} + 198 q^{14} - 4302 q^{16} - 522 q^{19} + 24 q^{25} + 678 q^{26} - 3952 q^{29} + 3600 q^{31} + 2266 q^{35} + 6642 q^{40} + 1802 q^{44} + 6678 q^{46} + 9492 q^{49} - 1992 q^{50} - 12564 q^{56} - 13908 q^{59} - 10296 q^{61} - 55596 q^{64} - 1912 q^{65} - 12468 q^{70} + 7640 q^{71} + 15054 q^{74} - 4044 q^{79} - 29748 q^{80} + 27108 q^{85} - 17988 q^{86} + 16764 q^{89} + 9216 q^{91} + 64638 q^{94} + 30540 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)