Properties

Label 34.2.a
Level 34
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(34))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 17
34.2.a.a \(1\) \(0.271\) \(\Q\) None \(1\) \(-2\) \(0\) \(-4\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-4q^{7}+q^{8}+\cdots\)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ \( 1 + 2 T + 3 T^{2} \)
$5$ \( 1 + 5 T^{2} \)
$7$ \( 1 + 4 T + 7 T^{2} \)
$11$ \( 1 - 6 T + 11 T^{2} \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 + T \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 + 4 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 - 8 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 + 6 T + 53 T^{2} \)
$59$ \( 1 + 59 T^{2} \)
$61$ \( 1 + 4 T + 61 T^{2} \)
$67$ \( 1 - 8 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 - 2 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 14 T + 97 T^{2} \)
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