Properties

Label 108.1.c
Level 108
Weight 1
Character orbit c
Rep. character \(\chi_{108}(53,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 108.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(108, [\chi])\).

Total New Old
Modular forms 10 1 9
Cusp forms 1 1 0
Eisenstein series 9 0 9

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

\( q - q^{7} + O(q^{10}) \) \( q - q^{7} - q^{13} - q^{19} + q^{25} + 2q^{31} - q^{37} + 2q^{43} - q^{61} - q^{67} - q^{73} - q^{79} + q^{91} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.1.c.a \(1\) \(0.054\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots\)

Hecke characteristic polynomials

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