Properties

Label 136.1.e
Level 136
Weight 1
Character orbit e
Rep. character \(\chi_{136}(67,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 136.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(136, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{2} + q^{4} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{8} + q^{9} + q^{16} - q^{17} - q^{18} - 2q^{19} - q^{25} - q^{32} + q^{34} + q^{36} + 2q^{38} + 2q^{43} - q^{49} + q^{50} + 2q^{59} + q^{64} - 2q^{67} - q^{68} - q^{72} - 2q^{76} + q^{81} + 2q^{83} - 2q^{86} - 2q^{89} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(136, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
136.1.e.a \(1\) \(0.068\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\)

Hecke characteristic polynomials

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