Properties

Label 103.1.b
Level 103
Weight 1
Character orbit b
Rep. character \(\chi_{103}(102,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 103 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 103.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(103, [\chi])\).

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

\( 2q - q^{2} + q^{4} - q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - q^{7} - 2q^{8} + 2q^{9} - q^{13} - 2q^{14} - q^{17} - q^{18} - q^{19} - q^{23} + 2q^{25} + 3q^{26} + 2q^{28} - q^{29} + 2q^{32} - 2q^{34} + q^{36} + 3q^{38} - q^{41} + 3q^{46} + q^{49} - q^{50} - 3q^{52} + q^{56} - 2q^{58} - q^{59} - q^{61} - q^{63} - q^{64} + 2q^{68} - 2q^{72} - 3q^{76} - q^{79} + 2q^{81} + 3q^{82} - q^{83} - 2q^{91} - 3q^{92} - q^{97} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(103, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
103.1.b.a \(2\) \(0.051\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-103}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)

Hecke characteristic polynomials

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