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Properties

Label 475.3.i
Level $475$
Weight $3$
Character orbit 475.i
Rep. character $\chi_{475}(274,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(150\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(475, [\chi])\).

Total New Old
Modular forms 212 124 88
Cusp forms 188 116 72
Eisenstein series 24 8 16

Trace form

\( 116 q - 114 q^{4} - 30 q^{6} - 160 q^{9} + O(q^{10}) \) \( 116 q - 114 q^{4} - 30 q^{6} - 160 q^{9} - 4 q^{11} - 12 q^{14} - 246 q^{16} + 44 q^{19} - 78 q^{21} - 154 q^{24} + 100 q^{26} + 66 q^{29} - 42 q^{34} - 136 q^{36} + 200 q^{39} + 66 q^{41} + 14 q^{44} - 636 q^{49} + 60 q^{51} - 560 q^{54} + 570 q^{59} - 102 q^{61} + 2188 q^{64} - 622 q^{66} + 84 q^{71} - 488 q^{74} - 176 q^{76} + 66 q^{79} + 62 q^{81} - 174 q^{86} - 588 q^{89} - 366 q^{91} + 236 q^{96} + 22 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)