Properties

Label 63.1
Level 63
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(63))\).

Total New Old
Modular forms 49 24 25
Cusp forms 1 1 0
Eisenstein series 48 23 25

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

\( q - q^{4} - q^{7} + O(q^{10}) \) \( q - q^{4} - q^{7} + q^{16} + q^{25} + q^{28} - 2q^{37} - 2q^{43} + q^{49} - q^{64} + 2q^{67} + 2q^{79} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.1.b \(\chi_{63}(8, \cdot)\) None 0 1
63.1.d \(\chi_{63}(55, \cdot)\) 63.1.d.a 1 1
63.1.j \(\chi_{63}(11, \cdot)\) None 0 2
63.1.k \(\chi_{63}(31, \cdot)\) None 0 2
63.1.l \(\chi_{63}(13, \cdot)\) None 0 2
63.1.m \(\chi_{63}(10, \cdot)\) None 0 2
63.1.n \(\chi_{63}(2, \cdot)\) None 0 2
63.1.q \(\chi_{63}(44, \cdot)\) None 0 2
63.1.r \(\chi_{63}(29, \cdot)\) None 0 2
63.1.t \(\chi_{63}(40, \cdot)\) None 0 2

Hecke characteristic polynomials

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