Properties

Label 475.2.x
Level $475$
Weight $2$
Character orbit 475.x
Rep. character $\chi_{475}(64,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $384$
Newform subspaces $1$
Sturm bound $100$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.x (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(100\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

Total New Old
Modular forms 416 416 0
Cusp forms 384 384 0
Eisenstein series 32 32 0

Trace form

\( 384 q - 5 q^{2} - 5 q^{3} - 49 q^{4} - 5 q^{5} + 5 q^{6} - 50 q^{8} - 47 q^{9} + O(q^{10}) \) \( 384 q - 5 q^{2} - 5 q^{3} - 49 q^{4} - 5 q^{5} + 5 q^{6} - 50 q^{8} - 47 q^{9} - 3 q^{10} - 6 q^{11} - 20 q^{12} - 5 q^{13} + q^{14} + 19 q^{15} + 35 q^{16} + 12 q^{20} + 26 q^{21} - 75 q^{22} - 35 q^{23} - 20 q^{24} + 5 q^{25} - 4 q^{26} - 50 q^{27} + 15 q^{28} - 21 q^{29} + 8 q^{30} - 36 q^{31} - 15 q^{33} - 3 q^{34} + 9 q^{35} + 19 q^{36} - 20 q^{37} - 75 q^{38} + 24 q^{39} - 40 q^{40} + 13 q^{41} + 25 q^{42} + 47 q^{44} + 132 q^{45} + 28 q^{46} - 75 q^{47} + 15 q^{48} - 300 q^{49} - 50 q^{50} - 70 q^{51} - 15 q^{52} - 25 q^{53} - 10 q^{54} + 70 q^{55} - 20 q^{56} + 290 q^{58} - 51 q^{59} + 26 q^{60} + 11 q^{61} - 30 q^{62} + 45 q^{63} - 2 q^{64} - 96 q^{65} + 13 q^{66} - 25 q^{67} + 24 q^{69} - 32 q^{70} + 38 q^{71} + 50 q^{72} - 85 q^{73} + 2 q^{74} + 116 q^{75} + 36 q^{76} + 160 q^{77} - 80 q^{78} - 19 q^{79} - 45 q^{80} - 65 q^{81} - 90 q^{83} - 44 q^{84} - 60 q^{85} + 35 q^{86} - 230 q^{87} + 100 q^{88} - 21 q^{89} - 143 q^{90} + 34 q^{91} + 5 q^{92} + 72 q^{94} + 58 q^{95} - 190 q^{96} + 10 q^{97} + 60 q^{98} + 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.2.x.a 475.x 475.x $384$ $3.793$ None \(-5\) \(-5\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{30}]$