Properties

Label 10.5
Level 10
Weight 5
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 30
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(10))\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 20 q^{3} - 60 q^{5} - 64 q^{6} + 20 q^{7} + 160 q^{10} + 168 q^{11} + 160 q^{12} - 60 q^{13} + 20 q^{15} - 256 q^{16} - 1020 q^{17} - 640 q^{18} + 968 q^{21} + 1280 q^{22} + 1620 q^{23} - 700 q^{25}+ \cdots + 3840 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
10.5.c \(\chi_{10}(3, \cdot)\) 10.5.c.a 2 2
10.5.c.b 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)