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Properties

Label 475.3.bj
Level $475$
Weight $3$
Character orbit 475.bj
Rep. character $\chi_{475}(17,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $4704$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.bj (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(150\)

Dimensions

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

Total New Old
Modular forms 4896 4896 0
Cusp forms 4704 4704 0
Eisenstein series 192 192 0

Trace form

\( 4704 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 42 q^{7} - 24 q^{8} - 60 q^{9} + O(q^{10}) \) \( 4704 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 42 q^{7} - 24 q^{8} - 60 q^{9} - 48 q^{10} - 18 q^{11} - 24 q^{12} - 48 q^{13} - 60 q^{14} - 66 q^{15} - 36 q^{16} - 102 q^{17} - 288 q^{18} - 60 q^{19} - 156 q^{20} - 36 q^{21} - 264 q^{22} + 48 q^{23} + 48 q^{25} - 48 q^{26} - 24 q^{27} + 372 q^{28} + 240 q^{29} - 24 q^{30} - 18 q^{31} + 330 q^{32} + 618 q^{33} - 60 q^{34} + 114 q^{35} - 36 q^{36} - 96 q^{37} - 924 q^{38} - 120 q^{39} - 1344 q^{40} - 36 q^{41} - 264 q^{42} + 1236 q^{43} - 60 q^{44} + 174 q^{45} - 18 q^{46} - 528 q^{47} - 1092 q^{48} + 264 q^{50} - 96 q^{51} + 48 q^{52} - 30 q^{53} - 60 q^{54} + 42 q^{55} - 72 q^{56} + 1986 q^{57} + 48 q^{58} + 1140 q^{59} - 912 q^{60} - 36 q^{61} - 3384 q^{62} - 42 q^{63} - 30 q^{64} + 1056 q^{65} - 468 q^{66} + 648 q^{67} - 360 q^{68} - 30 q^{69} - 720 q^{70} - 36 q^{71} - 204 q^{72} - 210 q^{73} + 576 q^{75} - 96 q^{76} - 1128 q^{77} - 1008 q^{78} - 60 q^{79} + 708 q^{80} - 36 q^{81} - 2064 q^{82} - 1758 q^{83} - 3630 q^{84} + 576 q^{85} - 36 q^{86} + 1944 q^{87} - 1152 q^{88} - 60 q^{89} - 3096 q^{90} - 36 q^{91} - 2100 q^{92} + 90 q^{93} - 120 q^{94} - 276 q^{95} - 72 q^{96} - 252 q^{97} + 966 q^{98} + O(q^{100}) \)

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.