Properties

Label 34.2.a
Level $34$
Weight $2$
Character orbit 34.a
Rep. character $\chi_{34}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 34 = 2 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 34.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(34))\).

Total New Old
Modular forms 6 1 5
Cusp forms 3 1 2
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.

\(2\)\(17\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 4 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 4 q^{7} + q^{8} + q^{9} + 6 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{16} - q^{17} + q^{18} - 4 q^{19} + 8 q^{21} + 6 q^{22} - 2 q^{24} - 5 q^{25} + 2 q^{26} + 4 q^{27} - 4 q^{28} - 4 q^{31} + q^{32} - 12 q^{33} - q^{34} + q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} + 6 q^{41} + 8 q^{42} + 8 q^{43} + 6 q^{44} - 2 q^{48} + 9 q^{49} - 5 q^{50} + 2 q^{51} + 2 q^{52} - 6 q^{53} + 4 q^{54} - 4 q^{56} + 8 q^{57} - 4 q^{61} - 4 q^{62} - 4 q^{63} + q^{64} - 12 q^{66} + 8 q^{67} - q^{68} + q^{72} + 2 q^{73} - 4 q^{74} + 10 q^{75} - 4 q^{76} - 24 q^{77} - 4 q^{78} + 8 q^{79} - 11 q^{81} + 6 q^{82} + 8 q^{84} + 8 q^{86} + 6 q^{88} - 6 q^{89} - 8 q^{91} + 8 q^{93} - 2 q^{96} + 14 q^{97} + 9 q^{98} + 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(34))\) 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 17
34.2.a.a 34.a 1.a $1$ $0.271$ \(\Q\) None \(1\) \(-2\) \(0\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(34))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(34)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)