Defining parameters
Level: | \( N \) | = | \( 3018 = 2 \cdot 3 \cdot 503 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(1012032\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3018))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 255016 | 63253 | 191763 |
Cusp forms | 251001 | 63253 | 187748 |
Eisenstein series | 4015 | 0 | 4015 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3018))\)
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 |
---|---|---|---|---|
3018.2.a | \(\chi_{3018}(1, \cdot)\) | 3018.2.a.a | 1 | 1 |
3018.2.a.b | 1 | |||
3018.2.a.c | 1 | |||
3018.2.a.d | 1 | |||
3018.2.a.e | 1 | |||
3018.2.a.f | 4 | |||
3018.2.a.g | 6 | |||
3018.2.a.h | 9 | |||
3018.2.a.i | 9 | |||
3018.2.a.j | 10 | |||
3018.2.a.k | 12 | |||
3018.2.a.l | 13 | |||
3018.2.a.m | 17 | |||
3018.2.d | \(\chi_{3018}(3017, \cdot)\) | n/a | 168 | 1 |
3018.2.e | \(\chi_{3018}(7, \cdot)\) | n/a | 21000 | 250 |
3018.2.f | \(\chi_{3018}(5, \cdot)\) | n/a | 42000 | 250 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3018))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1509))\)\(^{\oplus 2}\)