Properties

Label 201.2.e
Level 201
Weight 2
Character orbit e
Rep. character \(\chi_{201}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 22
Newforms 3
Sturm bound 45
Trace bound 2

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 50 22 28
Cusp forms 42 22 20
Eisenstein series 8 0 8

Trace form

\( 22q - 4q^{2} + 2q^{3} - 14q^{4} - 6q^{7} + 12q^{8} + 22q^{9} + O(q^{10}) \) \( 22q - 4q^{2} + 2q^{3} - 14q^{4} - 6q^{7} + 12q^{8} + 22q^{9} - 12q^{10} + 6q^{11} - 2q^{12} - 3q^{13} - 12q^{14} - 4q^{15} - 20q^{16} + 4q^{17} - 4q^{18} - 6q^{19} + 16q^{20} - 4q^{21} + 36q^{22} - 2q^{23} - 12q^{24} + 14q^{25} - 20q^{26} + 2q^{27} - 14q^{28} + 2q^{29} + 4q^{30} - 29q^{31} - 6q^{32} + 2q^{33} - 32q^{34} + 30q^{35} - 14q^{36} + 8q^{37} + 6q^{38} - 9q^{39} + 12q^{40} + 6q^{41} + 32q^{42} - 14q^{43} + 32q^{44} + 16q^{46} - 66q^{47} - 20q^{48} - 17q^{49} - 26q^{50} + 52q^{52} - 40q^{53} - 12q^{56} - 12q^{57} + 40q^{58} + 12q^{59} - 16q^{60} + 15q^{61} + 68q^{62} - 6q^{63} + 40q^{64} + 24q^{66} + 9q^{67} - 92q^{68} - 20q^{70} + 28q^{71} + 12q^{72} + 19q^{73} + 54q^{74} + 14q^{75} + 12q^{76} + 36q^{77} - 34q^{78} + 5q^{79} - 30q^{80} + 22q^{81} - 76q^{82} + 14q^{83} + 4q^{84} + 6q^{85} - 26q^{86} - 22q^{87} + 8q^{88} - 8q^{89} - 12q^{90} - 80q^{91} - 52q^{92} - 5q^{93} + 92q^{94} - 10q^{95} + 12q^{96} - 7q^{97} - 2q^{98} + 6q^{99} + O(q^{100}) \)

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.e.a \(2\) \(1.605\) \(\Q(\sqrt{-3}) \) None \(-2\) \(2\) \(-8\) \(-4\) \(q+(-2+2\zeta_{6})q^{2}+q^{3}-2\zeta_{6}q^{4}-4q^{5}+\cdots\)
201.2.e.b \(10\) \(1.605\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-10\) \(2\) \(-1\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
201.2.e.c \(10\) \(1.605\) 10.0.\(\cdots\).1 None \(0\) \(10\) \(6\) \(-1\) \(q+\beta _{9}q^{2}+q^{3}+(\beta _{1}-2\beta _{4}-2\beta _{5})q^{4}+\cdots\)

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

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