Properties

Label 134.2.a
Level 134
Weight 2
Character orbit a
Rep. character \(\chi_{134}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(134))\) into irreducible Hecke orbits

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

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