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Properties

Label 315.5.ba
Level $315$
Weight $5$
Character orbit 315.ba
Rep. character $\chi_{315}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 392 288 104
Cusp forms 376 288 88
Eisenstein series 16 0 16

Trace form

\( 288 q - 1152 q^{4} - 18 q^{5} + 208 q^{9} + O(q^{10}) \) \( 288 q - 1152 q^{4} - 18 q^{5} + 208 q^{9} - 234 q^{11} - 500 q^{15} - 9216 q^{16} + 4482 q^{20} - 98 q^{21} - 3972 q^{24} + 294 q^{25} + 728 q^{30} + 2220 q^{31} + 804 q^{34} - 2772 q^{36} + 646 q^{39} + 5256 q^{41} - 1278 q^{45} + 7224 q^{46} + 49392 q^{49} - 14958 q^{50} + 6998 q^{51} - 36540 q^{54} - 1452 q^{55} + 54684 q^{59} + 60576 q^{60} + 149304 q^{64} + 14256 q^{65} - 65960 q^{66} + 1660 q^{69} - 129276 q^{74} - 45660 q^{75} + 2652 q^{76} - 942 q^{79} + 61304 q^{81} + 6272 q^{84} - 14784 q^{85} - 23508 q^{86} - 8908 q^{90} - 11172 q^{91} + 39120 q^{94} - 68472 q^{95} + 62388 q^{96} - 102888 q^{99} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)