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Properties

Label 495.4.u
Level $495$
Weight $4$
Character orbit 495.u
Rep. character $\chi_{495}(34,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $360$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 495.u (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 \(M_{4}(495, [\chi])\).

Total New Old
Modular forms 440 360 80
Cusp forms 424 360 64
Eisenstein series 16 0 16

Trace form

\( 360 q + 720 q^{4} - 4 q^{5} - 16 q^{6} - 4 q^{9} + O(q^{10}) \) \( 360 q + 720 q^{4} - 4 q^{5} - 16 q^{6} - 4 q^{9} - 88 q^{11} + 136 q^{14} + 188 q^{15} - 2880 q^{16} + 218 q^{20} - 64 q^{21} - 124 q^{24} - 72 q^{25} + 1248 q^{26} - 84 q^{29} + 782 q^{30} + 36 q^{31} - 396 q^{34} + 1080 q^{35} - 792 q^{36} - 1280 q^{39} + 156 q^{41} - 1760 q^{44} - 1622 q^{45} + 1080 q^{46} + 9216 q^{49} - 926 q^{50} + 624 q^{51} + 2076 q^{54} - 396 q^{55} - 1632 q^{56} + 3516 q^{59} + 7778 q^{60} + 36 q^{61} - 24408 q^{64} - 232 q^{65} - 872 q^{69} + 12888 q^{71} + 4228 q^{74} - 1998 q^{75} - 1116 q^{76} - 1652 q^{80} - 52 q^{81} - 6852 q^{84} + 1656 q^{85} - 13676 q^{86} - 11192 q^{89} - 7652 q^{90} - 1224 q^{94} + 1308 q^{95} - 2264 q^{96} + 220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)