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Properties

Label 501.2.g
Level $501$
Weight $2$
Character orbit 501.g
Rep. character $\chi_{501}(5,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $4428$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 501 = 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 501.g (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q(\zeta_{166})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(501, [\chi])\).

Total New Old
Modular forms 4756 4756 0
Cusp forms 4428 4428 0
Eisenstein series 328 328 0

Trace form

\( 4428 q - 81 q^{3} - 106 q^{4} - 87 q^{6} - 162 q^{7} - 81 q^{9} + O(q^{10}) \) \( 4428 q - 81 q^{3} - 106 q^{4} - 87 q^{6} - 162 q^{7} - 81 q^{9} - 166 q^{10} - 73 q^{12} - 166 q^{13} - 83 q^{15} - 230 q^{16} - 85 q^{18} - 166 q^{19} - 55 q^{21} - 162 q^{22} - 113 q^{24} - 204 q^{25} - 57 q^{27} - 170 q^{28} - 83 q^{30} - 142 q^{31} - 63 q^{33} - 166 q^{34} - 59 q^{36} - 166 q^{37} - 83 q^{39} - 166 q^{40} - 88 q^{42} - 166 q^{43} - 83 q^{45} - 166 q^{46} - 72 q^{48} - 228 q^{49} - 83 q^{51} - 166 q^{52} - 106 q^{54} - 166 q^{55} - 43 q^{57} - 222 q^{58} - 83 q^{60} - 126 q^{61} - 77 q^{63} - 26 q^{64} - 79 q^{66} - 166 q^{67} - 83 q^{69} - 166 q^{70} - 64 q^{72} - 166 q^{73} - 139 q^{75} - 206 q^{76} - 83 q^{78} - 166 q^{79} - 41 q^{81} - 166 q^{82} - 164 q^{84} - 166 q^{85} - 81 q^{87} - 102 q^{88} - 83 q^{90} - 166 q^{91} - 47 q^{93} - 186 q^{94} - q^{96} - 198 q^{97} - 183 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(501, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
501.2.g.a 501.g 501.g $4428$ $4.001$ None \(0\) \(-81\) \(0\) \(-162\) $\mathrm{SU}(2)[C_{166}]$