Properties

Label 201.2.i
Level 201
Weight 2
Character orbit i
Rep. character \(\chi_{201}(22,\cdot)\)
Character field \(\Q(\zeta_{11})\)
Dimension 120
Newforms 2
Sturm bound 45
Trace bound 1

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Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 201.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{11})\)
Newforms: \( 2 \)
Sturm bound: \(45\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(201, [\chi])\).

Total New Old
Modular forms 240 120 120
Cusp forms 200 120 80
Eisenstein series 40 0 40

Trace form

\( 120q - 4q^{2} - 2q^{3} - 18q^{4} - 8q^{7} + 42q^{8} - 12q^{9} + O(q^{10}) \) \( 120q - 4q^{2} - 2q^{3} - 18q^{4} - 8q^{7} + 42q^{8} - 12q^{9} + 54q^{10} - 12q^{11} - 6q^{12} - 20q^{13} - 24q^{14} + 18q^{15} - 30q^{16} - 14q^{17} - 4q^{18} + 8q^{19} - 32q^{20} - 12q^{21} - 26q^{22} - 14q^{23} - 12q^{24} - 20q^{25} - 20q^{26} - 2q^{27} - 42q^{28} - 12q^{29} + 24q^{30} + 4q^{31} + 38q^{32} - 4q^{33} - 44q^{34} - 60q^{35} + 4q^{36} - 20q^{37} - 36q^{38} - 20q^{39} + 50q^{40} + 42q^{41} - 16q^{42} + 14q^{43} - 64q^{44} - 34q^{46} - 12q^{47} - 30q^{48} - 68q^{49} - 26q^{50} - 24q^{51} + 34q^{52} - 30q^{53} - 50q^{55} + 92q^{56} + 78q^{57} - 24q^{58} + 22q^{59} + 48q^{60} + 8q^{61} - 56q^{62} + 14q^{63} - 40q^{64} + 28q^{65} + 64q^{66} - 42q^{67} + 456q^{68} - 2q^{69} + 44q^{70} + 8q^{71} + 20q^{72} + 42q^{73} - 112q^{74} + 6q^{75} - 28q^{76} + 68q^{77} - 20q^{78} + 12q^{79} - 60q^{80} - 12q^{81} + 96q^{82} - 66q^{83} + 146q^{84} - 72q^{85} + 32q^{86} - 40q^{87} - 76q^{88} + 4q^{89} + 54q^{90} + 12q^{91} - 108q^{92} - 28q^{93} - 116q^{94} - 118q^{95} - 24q^{96} + 4q^{97} - 100q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(201, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
201.2.i.a \(50\) \(1.605\) None \(-2\) \(5\) \(2\) \(2\)
201.2.i.b \(70\) \(1.605\) None \(-2\) \(-7\) \(-2\) \(-10\)

Decomposition of \(S_{2}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)