Defining parameters
Level: | \( N \) | = | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(20))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 70 | 37 | 33 |
Cusp forms | 50 | 29 | 21 |
Eisenstein series | 20 | 8 | 12 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
20.6.a | \(\chi_{20}(1, \cdot)\) | 20.6.a.a | 1 | 1 |
20.6.c | \(\chi_{20}(9, \cdot)\) | 20.6.c.a | 2 | 1 |
20.6.e | \(\chi_{20}(3, \cdot)\) | 20.6.e.a | 2 | 2 |
20.6.e.b | 24 |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)