Defining parameters
Level: | \( N \) | = | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | = | \( 12 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(14))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 22 | 50 |
Cusp forms | 60 | 22 | 38 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(14))\)
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 |
---|---|---|---|---|
14.12.a | \(\chi_{14}(1, \cdot)\) | 14.12.a.a | 1 | 1 |
14.12.a.b | 1 | |||
14.12.a.c | 2 | |||
14.12.a.d | 2 | |||
14.12.c | \(\chi_{14}(9, \cdot)\) | 14.12.c.a | 8 | 2 |
14.12.c.b | 8 |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)