Defining parameters
Level: | \( N \) | = | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(12))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 29 | 8 | 21 |
Cusp forms | 19 | 8 | 11 |
Eisenstein series | 10 | 0 | 10 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
12.7.c | \(\chi_{12}(5, \cdot)\) | 12.7.c.a | 2 | 1 |
12.7.d | \(\chi_{12}(7, \cdot)\) | 12.7.d.a | 6 | 1 |
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)