Properties

Label 134.2.a
Level 134
Weight 2
Character orbit a
Rep. character \(\chi_{134}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 2
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(34\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(134))\).

Total New Old
Modular forms 19 6 13
Cusp forms 16 6 10
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(67\)FrickeDim.
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(6\)

Trace form

\( 6q + 4q^{3} + 6q^{4} + 2q^{6} + 8q^{9} + O(q^{10}) \) \( 6q + 4q^{3} + 6q^{4} + 2q^{6} + 8q^{9} - 6q^{10} - 4q^{11} + 4q^{12} + 8q^{13} - 8q^{15} + 6q^{16} - 6q^{17} - 8q^{18} + 12q^{19} - 12q^{21} - 2q^{22} - 14q^{23} + 2q^{24} + 4q^{25} - 14q^{26} - 8q^{27} - 12q^{29} - 16q^{30} + 16q^{31} - 32q^{33} - 20q^{35} + 8q^{36} + 4q^{37} - 16q^{39} - 6q^{40} - 4q^{41} + 4q^{43} - 4q^{44} - 12q^{45} + 8q^{46} + 22q^{47} + 4q^{48} + 22q^{49} + 8q^{50} + 8q^{51} + 8q^{52} - 12q^{53} + 20q^{54} + 16q^{55} + 20q^{57} - 12q^{58} - 8q^{60} + 36q^{61} + 8q^{62} - 20q^{63} + 6q^{64} + 12q^{65} + 8q^{66} - 6q^{68} + 16q^{69} + 20q^{70} + 14q^{71} - 8q^{72} - 14q^{73} - 4q^{74} + 64q^{75} + 12q^{76} + 8q^{77} + 4q^{78} + 4q^{79} + 6q^{81} + 4q^{82} - 4q^{83} - 12q^{84} - 28q^{85} + 2q^{86} - 12q^{87} - 2q^{88} + 22q^{89} - 42q^{90} + 16q^{91} - 14q^{92} - 20q^{93} + 20q^{94} + 2q^{96} + 16q^{97} - 16q^{98} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(134))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 67
134.2.a.a \(3\) \(1.070\) 3.3.473.1 None \(-3\) \(1\) \(3\) \(0\) \(+\) \(-\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
134.2.a.b \(3\) \(1.070\) \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(134))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(134)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)