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

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

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

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