Properties

Label 204.1
Level 204
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 2304
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 204 = 2^{2} \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(2304\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(204))\).

Total New Old
Modular forms 168 34 134
Cusp forms 8 2 6
Eisenstein series 160 32 128

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

\( 2q + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{9} - 2q^{13} - 2q^{15} - 2q^{19} - 2q^{33} - 2q^{43} + 2q^{49} + 2q^{51} + 2q^{55} + 4q^{67} - 2q^{69} + 2q^{81} - 2q^{85} + 4q^{87} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)

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
204.1.d \(\chi_{204}(137, \cdot)\) None 0 1
204.1.e \(\chi_{204}(67, \cdot)\) None 0 1
204.1.f \(\chi_{204}(103, \cdot)\) None 0 1
204.1.g \(\chi_{204}(101, \cdot)\) 204.1.g.a 1 1
204.1.g.b 1
204.1.i \(\chi_{204}(89, \cdot)\) None 0 2
204.1.k \(\chi_{204}(55, \cdot)\) None 0 2
204.1.m \(\chi_{204}(53, \cdot)\) None 0 4
204.1.n \(\chi_{204}(19, \cdot)\) None 0 4
204.1.s \(\chi_{204}(37, \cdot)\) None 0 8
204.1.t \(\chi_{204}(11, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(204))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(204)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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