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Properties

Label 134.2.c
Level 134
Weight 2
Character orbit c
Rep. character \(\chi_{134}(29,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 10
Newforms 3
Sturm bound 34
Trace bound 2

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Defining parameters

Level: \( N \) = \( 134 = 2 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 134.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 3 \)
Sturm bound: \(34\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(134, [\chi])\).

Total New Old
Modular forms 38 10 28
Cusp forms 30 10 20
Eisenstein series 8 0 8

Trace form

\( 10q - q^{2} + 6q^{3} - 5q^{4} + 3q^{6} + 2q^{7} + 2q^{8} + 8q^{9} + O(q^{10}) \) \( 10q - q^{2} + 6q^{3} - 5q^{4} + 3q^{6} + 2q^{7} + 2q^{8} + 8q^{9} - 2q^{11} - 3q^{12} - 6q^{13} - 8q^{14} - 16q^{15} - 5q^{16} + 3q^{17} - 2q^{18} - q^{19} + 2q^{21} + 20q^{22} - 10q^{23} - 6q^{24} - 18q^{25} + 30q^{27} + 2q^{28} - 6q^{29} - 2q^{30} - 14q^{31} - q^{32} + 2q^{33} + 3q^{34} + 14q^{35} - 4q^{36} + 16q^{37} - 5q^{38} - 24q^{39} - 2q^{41} - 20q^{42} - 14q^{43} - 2q^{44} - 48q^{45} + 10q^{46} - 4q^{47} - 3q^{48} + 5q^{49} + 9q^{50} + 13q^{51} + 12q^{52} + 36q^{53} - 15q^{54} + 8q^{55} + 4q^{56} - 3q^{57} + 12q^{58} - 6q^{59} + 8q^{60} + 8q^{61} + 8q^{62} - 8q^{63} + 10q^{64} + 18q^{65} + 40q^{66} + 34q^{67} - 6q^{68} + 2q^{69} - 8q^{70} - 14q^{71} + 4q^{72} + 25q^{73} - 10q^{74} - 6q^{75} + 2q^{76} - 14q^{77} + 22q^{79} - 14q^{81} + 20q^{82} - 56q^{83} + 2q^{84} + 16q^{85} - 7q^{86} - 6q^{87} - 10q^{88} + 26q^{89} - 6q^{90} + 20q^{92} - 26q^{93} + 40q^{94} - 30q^{95} + 3q^{96} + 25q^{97} - 17q^{98} - 16q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(134, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
134.2.c.a \(2\) \(1.070\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(4\) \(4\) \(q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+2q^{5}+\cdots\)
134.2.c.b \(4\) \(1.070\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-2\) \(2\) \(-4\) \(-1\) \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1})q^{4}+\cdots\)
134.2.c.c \(4\) \(1.070\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(2\) \(6\) \(0\) \(-1\) \(q+(1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)