Properties

Label 144.1.g
Level 144
Weight 1
Character orbit g
Rep. character \(\chi_{144}(127,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 144.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(144, [\chi])\).

Total New Old
Modular forms 13 1 12
Cusp forms 1 1 0
Eisenstein series 12 0 12

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

\( q + O(q^{10}) \) \( q - 2q^{13} - q^{25} + 2q^{37} + q^{49} + 2q^{61} - 2q^{73} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.1.g.a \(1\) \(0.072\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\)

Hecke characteristic polynomials

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