Properties

Label 49.22
Level 49
Weight 22
Dimension 1951
Nonzero newspaces 4
Sturm bound 4312
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(4312\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(49))\).

Total New Old
Modular forms 2088 2000 88
Cusp forms 2028 1951 77
Eisenstein series 60 49 11

Trace form

\( 1951 q - 303 q^{2} - 365055 q^{3} - 2014223 q^{4} + 23047071 q^{5} + 762701175 q^{6} - 758495850 q^{7} - 5045643909 q^{8} - 45914200230 q^{9} - 161657182545 q^{10} + 371608354605 q^{11} - 2598968961225 q^{12}+ \cdots + 11\!\cdots\!32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(49))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
49.22.a \(\chi_{49}(1, \cdot)\) 49.22.a.a 1 1
49.22.a.b 1
49.22.a.c 5
49.22.a.d 6
49.22.a.e 10
49.22.a.f 13
49.22.a.g 13
49.22.a.h 20
49.22.c \(\chi_{49}(18, \cdot)\) n/a 136 2
49.22.e \(\chi_{49}(8, \cdot)\) n/a 582 6
49.22.g \(\chi_{49}(2, \cdot)\) n/a 1164 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)