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Properties

Label 134.2.a
Level $134$
Weight $2$
Character orbit 134.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 67
134.2.a.a 134.a 1.a $3$ $1.070$ 3.3.473.1 None \(-3\) \(1\) \(3\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
134.2.a.b 134.a 1.a $3$ $1.070$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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