Defining parameters
Level: | \( N \) | = | \( 1004 = 2^{2} \cdot 251 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(126000\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1004))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32125 | 18625 | 13500 |
Cusp forms | 30876 | 18125 | 12751 |
Eisenstein series | 1249 | 500 | 749 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)
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 |
---|---|---|---|---|
1004.2.a | \(\chi_{1004}(1, \cdot)\) | 1004.2.a.a | 7 | 1 |
1004.2.a.b | 14 | |||
1004.2.c | \(\chi_{1004}(1003, \cdot)\) | n/a | 124 | 1 |
1004.2.e | \(\chi_{1004}(113, \cdot)\) | 1004.2.e.a | 84 | 4 |
1004.2.g | \(\chi_{1004}(231, \cdot)\) | n/a | 496 | 4 |
1004.2.i | \(\chi_{1004}(5, \cdot)\) | n/a | 420 | 20 |
1004.2.j | \(\chi_{1004}(47, \cdot)\) | n/a | 2480 | 20 |
1004.2.m | \(\chi_{1004}(9, \cdot)\) | n/a | 2100 | 100 |
1004.2.o | \(\chi_{1004}(11, \cdot)\) | n/a | 12400 | 100 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1004))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 2}\)