↑

Properties

Label 78.2
Level 78
Weight 2
Dimension 43
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 672
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(672\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(78))\).

Total New Old
Modular forms 216 43 173
Cusp forms 121 43 78
Eisenstein series 95 0 95

Trace form

\( 43 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} - 5 q^{8} - 3 q^{9} - 24 q^{10} - 12 q^{11} - 3 q^{12} - 35 q^{13} - 16 q^{14} - 18 q^{15} - 7 q^{16} - 12 q^{17} - 5 q^{18} - 36 q^{19} - 20 q^{21} + 12 q^{22}+ \cdots + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)

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
78.2.a \(\chi_{78}(1, \cdot)\) 78.2.a.a 1 1
78.2.b \(\chi_{78}(25, \cdot)\) 78.2.b.a 2 1
78.2.e \(\chi_{78}(55, \cdot)\) 78.2.e.a 2 2
78.2.e.b 2
78.2.g \(\chi_{78}(5, \cdot)\) 78.2.g.a 12 2
78.2.i \(\chi_{78}(43, \cdot)\) 78.2.i.a 4 2
78.2.i.b 4
78.2.k \(\chi_{78}(11, \cdot)\) 78.2.k.a 16 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(78))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(78)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)