Properties

Label 61.2.f
Level 61
Weight 2
Character orbit f
Rep. character \(\chi_{61}(14,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 10
Newform subspaces 2
Sturm bound 10
Trace bound 1

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Defining parameters

Level: \( N \) = \( 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 61.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 61 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(61, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10q - 3q^{2} - 6q^{3} + 9q^{4} + 3q^{5} - 15q^{6} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 10q - 3q^{2} - 6q^{3} + 9q^{4} + 3q^{5} - 15q^{6} - 9q^{7} + 4q^{9} + 3q^{10} - q^{12} - q^{13} - 15q^{16} - 6q^{17} + 9q^{18} + 5q^{19} + 24q^{20} + 18q^{21} - q^{22} - 8q^{25} - 21q^{26} - 6q^{27} - 3q^{29} - 60q^{30} - 21q^{31} + 39q^{32} + 32q^{34} + 21q^{35} + 36q^{36} + 14q^{39} + 12q^{40} - 18q^{41} + 15q^{42} + 6q^{43} - 12q^{44} + 6q^{45} - 17q^{46} - 32q^{48} - 8q^{49} + 12q^{51} - 8q^{52} - 30q^{54} + 12q^{55} - 4q^{57} + 28q^{58} - 9q^{59} - 9q^{61} + 102q^{62} - 42q^{63} - 100q^{64} + 30q^{65} + 22q^{66} - 21q^{67} - 69q^{68} - 72q^{70} - 3q^{71} - 9q^{73} + 3q^{74} + 21q^{75} + 19q^{76} - 9q^{77} + 45q^{78} + 24q^{79} + 57q^{80} - 14q^{81} + 51q^{82} - 48q^{83} - 48q^{86} + 21q^{87} + 96q^{88} + 72q^{90} - 12q^{91} - 69q^{92} - 12q^{93} + 42q^{95} + 120q^{96} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(61, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
61.2.f.a \(2\) \(0.487\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-4\) \(-3\) \(-6\) \(q+(-1-\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)
61.2.f.b \(8\) \(0.487\) 8.0.542936601.2 None \(0\) \(-2\) \(6\) \(-3\) \(q+(\beta _{1}+\beta _{6})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)