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Properties

Label 473.2.v
Level $473$
Weight $2$
Character orbit 473.v
Rep. character $\chi_{473}(4,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $1008$
Newform subspaces $1$
Sturm bound $88$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 473 = 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 473.v (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{35})\)
Newform subspaces: \( 1 \)
Sturm bound: \(88\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(473, [\chi])\).

Total New Old
Modular forms 1104 1104 0
Cusp forms 1008 1008 0
Eisenstein series 96 96 0

Trace form

\( 1008 q - 21 q^{2} - 19 q^{3} + 21 q^{4} - 19 q^{5} - 38 q^{6} - 6 q^{7} - 63 q^{8} + 11 q^{9} + O(q^{10}) \) \( 1008 q - 21 q^{2} - 19 q^{3} + 21 q^{4} - 19 q^{5} - 38 q^{6} - 6 q^{7} - 63 q^{8} + 11 q^{9} - 64 q^{10} - 24 q^{11} - 60 q^{12} + 8 q^{13} + 3 q^{14} - 7 q^{15} + 49 q^{16} - 23 q^{17} + 37 q^{18} - 76 q^{19} - 15 q^{20} - 10 q^{21} - 29 q^{22} - 106 q^{23} - 20 q^{24} + 27 q^{25} - 21 q^{26} - 13 q^{27} + 23 q^{28} - 43 q^{29} + 97 q^{30} - 25 q^{31} + 12 q^{32} - 66 q^{33} + 30 q^{34} + 85 q^{35} - 212 q^{36} - 92 q^{37} - 149 q^{38} - 79 q^{39} + 87 q^{40} - 45 q^{41} + 100 q^{42} + 26 q^{43} - 340 q^{44} + 18 q^{45} + 105 q^{46} - 27 q^{47} - 99 q^{48} - 194 q^{49} + 108 q^{50} + 53 q^{51} + 25 q^{52} - 79 q^{53} - 50 q^{54} + 44 q^{55} + 66 q^{56} - 57 q^{57} - 7 q^{58} + 71 q^{59} - 21 q^{60} - 50 q^{61} + 45 q^{62} + 161 q^{63} - 255 q^{64} + 28 q^{65} + 122 q^{66} - 14 q^{67} - 338 q^{68} - 83 q^{69} - 92 q^{70} + 23 q^{71} - 55 q^{72} - 29 q^{73} + 105 q^{74} - 54 q^{75} + 20 q^{76} + 4 q^{77} + 98 q^{78} + 96 q^{79} - 36 q^{80} - 156 q^{81} + 137 q^{82} - 4 q^{83} + 16 q^{84} - 236 q^{85} - 133 q^{86} + 20 q^{87} + 269 q^{88} + 50 q^{89} + 143 q^{90} + 23 q^{91} + 164 q^{92} + 66 q^{93} - 273 q^{94} - 85 q^{95} + 291 q^{96} - 44 q^{97} + 10 q^{98} - 129 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(473, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
473.2.v.a 473.v 473.v $1008$ $3.777$ None 473.2.v.a \(-21\) \(-19\) \(-19\) \(-6\) $\mathrm{SU}(2)[C_{35}]$