Defining parameters
Level: | \( N \) | = | \( 1002 = 2 \cdot 3 \cdot 167 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(111552\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1002))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28552 | 6973 | 21579 |
Cusp forms | 27225 | 6973 | 20252 |
Eisenstein series | 1327 | 0 | 1327 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)
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 |
---|---|---|---|---|
1002.2.a | \(\chi_{1002}(1, \cdot)\) | 1002.2.a.a | 1 | 1 |
1002.2.a.b | 1 | |||
1002.2.a.c | 1 | |||
1002.2.a.d | 1 | |||
1002.2.a.e | 1 | |||
1002.2.a.f | 2 | |||
1002.2.a.g | 3 | |||
1002.2.a.h | 3 | |||
1002.2.a.i | 4 | |||
1002.2.a.j | 5 | |||
1002.2.a.k | 7 | |||
1002.2.d | \(\chi_{1002}(1001, \cdot)\) | 1002.2.d.a | 56 | 1 |
1002.2.e | \(\chi_{1002}(7, \cdot)\) | n/a | 2296 | 82 |
1002.2.f | \(\chi_{1002}(5, \cdot)\) | n/a | 4592 | 82 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 2}\)