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Properties

Label 475.3.w
Level $475$
Weight $3$
Character orbit 475.w
Rep. character $\chi_{475}(58,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(150\)

Dimensions

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

Total New Old
Modular forms 816 720 96
Cusp forms 784 720 64
Eisenstein series 32 0 32

Trace form

\( 720 q + 4 q^{2} + 4 q^{3} + 6 q^{5} + 10 q^{7} - 24 q^{8} + O(q^{10}) \) \( 720 q + 4 q^{2} + 4 q^{3} + 6 q^{5} + 10 q^{7} - 24 q^{8} + 4 q^{10} - 16 q^{12} - 4 q^{13} + 16 q^{15} + 720 q^{16} - 44 q^{17} - 240 q^{18} - 320 q^{20} + 48 q^{22} - 68 q^{23} - 18 q^{25} - 40 q^{26} + 64 q^{27} + 464 q^{28} + 200 q^{30} + 328 q^{32} + 208 q^{33} + 500 q^{34} - 68 q^{35} - 1080 q^{36} + 12 q^{37} - 96 q^{40} + 160 q^{41} - 1336 q^{42} - 118 q^{43} - 72 q^{45} + 250 q^{47} - 464 q^{48} + 532 q^{50} + 432 q^{52} + 264 q^{53} + 1300 q^{54} + 88 q^{55} + 192 q^{58} - 300 q^{59} + 1164 q^{60} - 240 q^{61} - 1032 q^{62} - 750 q^{63} - 1600 q^{64} + 288 q^{65} - 92 q^{67} - 560 q^{68} - 700 q^{69} - 900 q^{70} + 120 q^{71} + 260 q^{72} + 50 q^{73} - 112 q^{75} - 274 q^{77} + 1288 q^{78} + 400 q^{79} + 1340 q^{81} - 552 q^{82} + 736 q^{83} - 2400 q^{84} - 1688 q^{85} - 216 q^{87} + 1844 q^{88} + 596 q^{90} + 296 q^{92} - 92 q^{93} - 1600 q^{94} + 38 q^{95} - 312 q^{97} - 676 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)