Defining parameters
Level: | \( N \) | = | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | = | \( 18 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(2304\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(48))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1116 | 463 | 653 |
Cusp forms | 1060 | 455 | 605 |
Eisenstein series | 56 | 8 | 48 |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(48))\)
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 |
---|---|---|---|---|
48.18.a | \(\chi_{48}(1, \cdot)\) | 48.18.a.a | 1 | 1 |
48.18.a.b | 1 | |||
48.18.a.c | 1 | |||
48.18.a.d | 1 | |||
48.18.a.e | 1 | |||
48.18.a.f | 1 | |||
48.18.a.g | 2 | |||
48.18.a.h | 2 | |||
48.18.a.i | 2 | |||
48.18.a.j | 2 | |||
48.18.a.k | 3 | |||
48.18.c | \(\chi_{48}(47, \cdot)\) | 48.18.c.a | 2 | 1 |
48.18.c.b | 12 | |||
48.18.c.c | 20 | |||
48.18.d | \(\chi_{48}(25, \cdot)\) | None | 0 | 1 |
48.18.f | \(\chi_{48}(23, \cdot)\) | None | 0 | 1 |
48.18.j | \(\chi_{48}(13, \cdot)\) | n/a | 136 | 2 |
48.18.k | \(\chi_{48}(11, \cdot)\) | n/a | 268 | 2 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces
\( S_{18}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 1}\)