Properties

Label 6.22
Level 6
Weight 22
Dimension 3
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 44
Trace bound 0

Downloads

Learn more

Defining parameters

Level: N N = 6=23 6 = 2 \cdot 3
Weight: k k = 22 22
Nonzero newspaces: 1 1
Newform subspaces: 3 3
Sturm bound: 4444
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M22(Γ1(6))M_{22}(\Gamma_1(6)).

Total New Old
Modular forms 23 3 20
Cusp forms 19 3 16
Eisenstein series 4 0 4

Trace form

3q+1024q2+59049q3+3145728q4+16153674q560466176q61636375008q7+1073741824q8+10460353203q937617076224q1098395423908q11+61917364224q12+34 ⁣ ⁣08q99+O(q100) 3 q + 1024 q^{2} + 59049 q^{3} + 3145728 q^{4} + 16153674 q^{5} - 60466176 q^{6} - 1636375008 q^{7} + 1073741824 q^{8} + 10460353203 q^{9} - 37617076224 q^{10} - 98395423908 q^{11} + 61917364224 q^{12}+ \cdots - 34\!\cdots\!08 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S22new(Γ1(6))S_{22}^{\mathrm{new}}(\Gamma_1(6))

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

Label χ\chi Newforms Dimension χ\chi degree
6.22.a χ6(1,)\chi_{6}(1, \cdot) 6.22.a.a 1 1
6.22.a.b 1
6.22.a.c 1

Decomposition of S22old(Γ1(6))S_{22}^{\mathrm{old}}(\Gamma_1(6)) into lower level spaces

S22old(Γ1(6)) S_{22}^{\mathrm{old}}(\Gamma_1(6)) \cong S22new(Γ1(1))S_{22}^{\mathrm{new}}(\Gamma_1(1))4^{\oplus 4}\oplusS22new(Γ1(2))S_{22}^{\mathrm{new}}(\Gamma_1(2))2^{\oplus 2}\oplusS22new(Γ1(3))S_{22}^{\mathrm{new}}(\Gamma_1(3))2^{\oplus 2}