Properties

Label 201.2.f
Level 201
Weight 2
Character orbit f
Rep. character \(\chi_{201}(38,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 42
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.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{6})\)
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 50 50 0
Cusp forms 42 42 0
Eisenstein series 8 8 0

Trace form

\( 42q - 22q^{4} - 2q^{6} + 2q^{9} + O(q^{10}) \) \( 42q - 22q^{4} - 2q^{6} + 2q^{9} - 6q^{10} + 15q^{12} - 3q^{13} - 26q^{15} - 40q^{16} + 6q^{18} + 2q^{19} + 12q^{21} + 52q^{22} - 26q^{24} + 30q^{25} - 60q^{28} + 57q^{30} - 51q^{31} + 8q^{33} - 12q^{34} - 4q^{36} + 2q^{37} + 14q^{39} - 40q^{40} + 30q^{46} - 66q^{48} - q^{49} - 12q^{51} + 20q^{54} - 16q^{55} - 24q^{57} + 80q^{60} + 15q^{61} + 6q^{63} + 120q^{64} - q^{67} - 21q^{69} + q^{73} + 84q^{76} - 42q^{78} - 9q^{79} - 6q^{81} + 104q^{82} + 27q^{84} - 78q^{85} - 21q^{87} - 62q^{88} - 110q^{90} - 20q^{91} + 2q^{93} - 9q^{96} - 99q^{97} + 87q^{99} + O(q^{100}) \)

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.f.a \(2\) \(1.605\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(6\) \(q+(1-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(4-2\zeta_{6})q^{7}+\cdots\)
201.2.f.b \(40\) \(1.605\) None \(0\) \(0\) \(0\) \(-6\)