Properties

Label 31.1
Level 31
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 80
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(31))\).

Total New Old
Modular forms 16 16 0
Cusp forms 1 1 0
Eisenstein series 15 15 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

\( q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + q^{10} + q^{14} - q^{16} - q^{18} - q^{19} + q^{31} + q^{35} + q^{38} - q^{40} - q^{41} - q^{45} + 2q^{47} - q^{56} - q^{59} - q^{62} - q^{63} + q^{64} + 2q^{67} - q^{70} - q^{71} + q^{72} + q^{80} + q^{81} + q^{82} + q^{90} - 2q^{94} + q^{95} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)

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
31.1.b \(\chi_{31}(30, \cdot)\) 31.1.b.a 1 1
31.1.e \(\chi_{31}(6, \cdot)\) None 0 2
31.1.f \(\chi_{31}(15, \cdot)\) None 0 4
31.1.h \(\chi_{31}(3, \cdot)\) None 0 8

Hecke characteristic polynomials

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