Defining parameters
Level: | \( N \) | = | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 28 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(4200\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(50))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2053 | 623 | 1430 |
Cusp forms | 1997 | 623 | 1374 |
Eisenstein series | 56 | 0 | 56 |
Trace form
Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(50))\)
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 |
---|---|---|---|---|
50.28.a | \(\chi_{50}(1, \cdot)\) | 50.28.a.a | 1 | 1 |
50.28.a.b | 1 | |||
50.28.a.c | 2 | |||
50.28.a.d | 2 | |||
50.28.a.e | 2 | |||
50.28.a.f | 3 | |||
50.28.a.g | 4 | |||
50.28.a.h | 4 | |||
50.28.a.i | 5 | |||
50.28.a.j | 5 | |||
50.28.a.k | 7 | |||
50.28.a.l | 7 | |||
50.28.b | \(\chi_{50}(49, \cdot)\) | 50.28.b.a | 2 | 1 |
50.28.b.b | 2 | |||
50.28.b.c | 4 | |||
50.28.b.d | 4 | |||
50.28.b.e | 4 | |||
50.28.b.f | 6 | |||
50.28.b.g | 8 | |||
50.28.b.h | 10 | |||
50.28.d | \(\chi_{50}(11, \cdot)\) | n/a | 268 | 4 |
50.28.e | \(\chi_{50}(9, \cdot)\) | n/a | 272 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces
\( S_{28}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)