Properties

Label 74.2
Level 74
Weight 2
Dimension 56
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 684
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 74 = 2 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(684\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(74))\).

Total New Old
Modular forms 207 56 151
Cusp forms 136 56 80
Eisenstein series 71 0 71

Trace form

\( 56 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)

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
74.2.a \(\chi_{74}(1, \cdot)\) 74.2.a.a 2 1
74.2.a.b 2
74.2.b \(\chi_{74}(73, \cdot)\) 74.2.b.a 4 1
74.2.c \(\chi_{74}(47, \cdot)\) 74.2.c.a 2 2
74.2.c.b 2
74.2.c.c 6
74.2.e \(\chi_{74}(11, \cdot)\) 74.2.e.a 4 2
74.2.e.b 4
74.2.f \(\chi_{74}(7, \cdot)\) 74.2.f.a 6 6
74.2.f.b 12
74.2.h \(\chi_{74}(3, \cdot)\) 74.2.h.a 12 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)