Defining parameters
Level: | \( N \) | = | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(446208\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2004))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 113212 | 49128 | 64084 |
Cusp forms | 109893 | 48472 | 61421 |
Eisenstein series | 3319 | 656 | 2663 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
2004.2.a | \(\chi_{2004}(1, \cdot)\) | 2004.2.a.a | 5 | 1 |
2004.2.a.b | 5 | |||
2004.2.a.c | 9 | |||
2004.2.a.d | 9 | |||
2004.2.b | \(\chi_{2004}(667, \cdot)\) | n/a | 168 | 1 |
2004.2.c | \(\chi_{2004}(335, \cdot)\) | n/a | 332 | 1 |
2004.2.h | \(\chi_{2004}(1001, \cdot)\) | 2004.2.h.a | 56 | 1 |
2004.2.i | \(\chi_{2004}(25, \cdot)\) | n/a | 2296 | 82 |
2004.2.j | \(\chi_{2004}(5, \cdot)\) | n/a | 4592 | 82 |
2004.2.o | \(\chi_{2004}(11, \cdot)\) | n/a | 27224 | 82 |
2004.2.p | \(\chi_{2004}(43, \cdot)\) | n/a | 13776 | 82 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2004))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 2}\)