Properties

Label 501.2.e
Level $501$
Weight $2$
Character orbit 501.e
Rep. character $\chi_{501}(4,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $2296$
Newform subspaces $2$
Sturm bound $112$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 501 = 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 501.e (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 4756 2296 2460
Cusp forms 4428 2296 2132
Eisenstein series 328 0 328

Trace form

\( 2296q - 32q^{4} - 4q^{6} - 28q^{9} + O(q^{10}) \) \( 2296q - 32q^{4} - 4q^{6} - 28q^{9} - 16q^{10} - 12q^{11} - 8q^{12} - 12q^{13} - 32q^{14} - 8q^{15} - 64q^{16} - 16q^{17} - 24q^{19} - 36q^{20} - 36q^{22} - 16q^{23} - 12q^{24} - 40q^{25} - 64q^{26} - 36q^{28} - 20q^{29} - 28q^{30} - 24q^{31} - 40q^{32} - 8q^{33} - 56q^{34} - 44q^{35} - 32q^{36} - 24q^{37} - 80q^{38} - 16q^{39} - 132q^{40} - 52q^{41} - 20q^{42} - 60q^{43} - 84q^{44} - 80q^{46} - 60q^{47} - 32q^{48} - 68q^{49} - 80q^{50} - 20q^{51} - 72q^{52} - 56q^{53} - 4q^{54} - 96q^{55} - 116q^{56} - 8q^{57} - 44q^{58} - 92q^{59} - 48q^{60} - 64q^{61} - 76q^{62} - 128q^{64} - 68q^{65} - 16q^{66} - 60q^{67} - 172q^{68} - 28q^{69} - 136q^{70} - 108q^{71} - 40q^{73} - 108q^{74} - 24q^{75} - 120q^{76} - 96q^{77} - 40q^{78} - 104q^{79} - 144q^{80} - 28q^{81} - 164q^{82} - 120q^{83} - 40q^{84} - 84q^{85} - 56q^{86} - 40q^{87} - 176q^{88} - 84q^{89} - 16q^{90} - 104q^{91} - 108q^{92} - 136q^{94} - 152q^{95} - 88q^{96} - 52q^{97} - 112q^{98} - 12q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
501.2.e.a \(1148\) \(4.001\) None \(-2\) \(-14\) \(-4\) \(0\)
501.2.e.b \(1148\) \(4.001\) None \(2\) \(14\) \(4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(501, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(501, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 2}\)