Defining parameters
Level: | \( N \) | = | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(4048128\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6036))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1017052 | 443760 | 573292 |
Cusp forms | 1007013 | 441760 | 565253 |
Eisenstein series | 10039 | 2000 | 8039 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6036))\)
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 |
---|---|---|---|---|
6036.2.a | \(\chi_{6036}(1, \cdot)\) | 6036.2.a.a | 1 | 1 |
6036.2.a.b | 1 | |||
6036.2.a.c | 1 | |||
6036.2.a.d | 1 | |||
6036.2.a.e | 1 | |||
6036.2.a.f | 14 | |||
6036.2.a.g | 15 | |||
6036.2.a.h | 24 | |||
6036.2.a.i | 26 | |||
6036.2.b | \(\chi_{6036}(2011, \cdot)\) | n/a | 504 | 1 |
6036.2.c | \(\chi_{6036}(1007, \cdot)\) | n/a | 1004 | 1 |
6036.2.h | \(\chi_{6036}(3017, \cdot)\) | n/a | 168 | 1 |
6036.2.i | \(\chi_{6036}(13, \cdot)\) | n/a | 21000 | 250 |
6036.2.j | \(\chi_{6036}(5, \cdot)\) | n/a | 42000 | 250 |
6036.2.o | \(\chi_{6036}(11, \cdot)\) | n/a | 251000 | 250 |
6036.2.p | \(\chi_{6036}(19, \cdot)\) | n/a | 126000 | 250 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6036))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1509))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3018))\)\(^{\oplus 2}\)