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Properties

Label 475.3.k
Level $475$
Weight $3$
Character orbit 475.k
Rep. character $\chi_{475}(126,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $122$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
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 212 134 78
Cusp forms 188 122 66
Eisenstein series 24 12 12

Trace form

\( 122 q + 3 q^{2} - 3 q^{3} + 123 q^{4} + 3 q^{6} + 20 q^{7} + 178 q^{9} + O(q^{10}) \) \( 122 q + 3 q^{2} - 3 q^{3} + 123 q^{4} + 3 q^{6} + 20 q^{7} + 178 q^{9} - 18 q^{11} + 36 q^{13} - 102 q^{14} - 261 q^{16} - 44 q^{17} - 51 q^{19} - 72 q^{21} + 39 q^{22} - 2 q^{23} + 87 q^{24} + 184 q^{26} + 76 q^{28} + 54 q^{29} + 99 q^{32} + 147 q^{33} + 48 q^{34} - 242 q^{36} - 72 q^{38} + 92 q^{39} + 129 q^{41} - 30 q^{42} + 54 q^{43} + 105 q^{44} - 138 q^{47} + 9 q^{48} + 470 q^{49} - 108 q^{51} + 192 q^{52} + 12 q^{53} + 65 q^{54} - 152 q^{57} - 152 q^{58} - 225 q^{59} - 24 q^{61} - 188 q^{62} - 8 q^{63} - 1294 q^{64} - 187 q^{66} - 105 q^{67} - 496 q^{68} - 198 q^{71} - 582 q^{72} + 301 q^{73} + 246 q^{74} - 13 q^{76} + 212 q^{77} - 210 q^{78} - 414 q^{79} - 521 q^{81} - 73 q^{82} - 762 q^{83} + 156 q^{86} + 628 q^{87} + 348 q^{89} + 6 q^{91} + 128 q^{92} + 384 q^{93} + 562 q^{96} - 231 q^{97} + 495 q^{98} + 110 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)