Properties

Label 104.1.h
Level 104
Weight 1
Character orbit h
Rep. character \(\chi_{104}(51,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 14
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 104.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(104, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 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 2 0 0 0

Trace form

\( 2q - 2q^{3} + 2q^{4} + O(q^{10}) \) \( 2q - 2q^{3} + 2q^{4} - 2q^{10} - 2q^{12} - 2q^{14} + 2q^{16} - 2q^{17} + 2q^{26} + 2q^{27} + 2q^{30} + 2q^{35} - 2q^{40} + 2q^{42} - 2q^{43} - 2q^{48} + 2q^{51} - 2q^{56} + 4q^{62} + 2q^{64} - 2q^{65} - 2q^{68} - 2q^{74} - 2q^{78} - 2q^{81} - 2q^{91} - 2q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(104, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
104.1.h.a \(1\) \(0.052\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-26}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
104.1.h.b \(1\) \(0.052\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-26}) \) None \(1\) \(-1\) \(-1\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)

Hecke characteristic polynomials

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