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Properties

Label 475.3.q
Level $475$
Weight $3$
Character orbit 475.q
Rep. character $\chi_{475}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $232$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.q (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(150\)

Dimensions

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

Total New Old
Modular forms 424 248 176
Cusp forms 376 232 144
Eisenstein series 48 16 32

Trace form

\( 232 q + 2 q^{2} + 2 q^{3} - 28 q^{6} + 20 q^{7} + 36 q^{8} + O(q^{10}) \) \( 232 q + 2 q^{2} + 2 q^{3} - 28 q^{6} + 20 q^{7} + 36 q^{8} - 48 q^{11} + 28 q^{12} + 10 q^{13} + 500 q^{16} + 34 q^{17} + 144 q^{18} + 8 q^{21} - 66 q^{22} - 82 q^{23} - 464 q^{26} + 128 q^{27} + 88 q^{28} + 296 q^{31} - 140 q^{32} + 104 q^{33} - 1028 q^{36} - 120 q^{37} - 234 q^{38} + 140 q^{41} + 158 q^{42} - 152 q^{43} - 448 q^{46} - 4 q^{47} - 132 q^{48} + 276 q^{51} + 138 q^{52} + 84 q^{53} + 240 q^{56} - 108 q^{57} - 324 q^{58} - 80 q^{61} + 204 q^{62} - 350 q^{63} + 716 q^{66} + 554 q^{67} + 908 q^{68} - 68 q^{71} - 416 q^{72} + 38 q^{73} + 1072 q^{76} + 652 q^{77} - 476 q^{78} + 288 q^{81} - 260 q^{82} - 884 q^{83} - 508 q^{86} - 1596 q^{87} + 456 q^{88} - 440 q^{91} - 716 q^{92} + 196 q^{93} - 1632 q^{96} + 124 q^{97} - 156 q^{98} + O(q^{100}) \)

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

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