Properties

Label 23.1
Level 23
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 44
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(44\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(23))\).

Total New Old
Modular forms 12 12 0
Cusp forms 1 1 0
Eisenstein series 11 11 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

\( q - q^{2} - q^{3} + q^{6} + q^{8} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{6} + q^{8} - q^{13} - q^{16} + q^{23} - q^{24} + q^{25} + q^{26} + q^{27} - q^{29} - q^{31} + q^{39} - q^{41} - q^{46} - q^{47} + q^{48} + q^{49} - q^{50} - q^{54} + q^{58} + 2q^{59} + q^{62} + q^{64} - q^{69} - q^{71} - q^{73} - q^{75} - q^{78} - q^{81} + q^{82} + q^{87} + q^{93} + q^{94} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.1.b \(\chi_{23}(22, \cdot)\) 23.1.b.a 1 1
23.1.d \(\chi_{23}(5, \cdot)\) None 0 10

Hecke characteristic polynomials

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