Defining parameters
Level: | \( N \) | = | \( 3006 = 2 \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(1003968\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3006))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 253648 | 66230 | 187418 |
Cusp forms | 248337 | 66230 | 182107 |
Eisenstein series | 5311 | 0 | 5311 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3006))\)
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 |
---|---|---|---|---|
3006.2.a | \(\chi_{3006}(1, \cdot)\) | 3006.2.a.a | 1 | 1 |
3006.2.a.b | 1 | |||
3006.2.a.c | 1 | |||
3006.2.a.d | 1 | |||
3006.2.a.e | 1 | |||
3006.2.a.f | 1 | |||
3006.2.a.g | 2 | |||
3006.2.a.h | 2 | |||
3006.2.a.i | 2 | |||
3006.2.a.j | 2 | |||
3006.2.a.k | 2 | |||
3006.2.a.l | 2 | |||
3006.2.a.m | 2 | |||
3006.2.a.n | 2 | |||
3006.2.a.o | 3 | |||
3006.2.a.p | 3 | |||
3006.2.a.q | 3 | |||
3006.2.a.r | 3 | |||
3006.2.a.s | 4 | |||
3006.2.a.t | 5 | |||
3006.2.a.u | 7 | |||
3006.2.a.v | 10 | |||
3006.2.a.w | 10 | |||
3006.2.d | \(\chi_{3006}(3005, \cdot)\) | 3006.2.d.a | 56 | 1 |
3006.2.e | \(\chi_{3006}(1003, \cdot)\) | n/a | 332 | 2 |
3006.2.f | \(\chi_{3006}(1001, \cdot)\) | n/a | 336 | 2 |
3006.2.i | \(\chi_{3006}(19, \cdot)\) | n/a | 5740 | 82 |
3006.2.j | \(\chi_{3006}(17, \cdot)\) | n/a | 4592 | 82 |
3006.2.m | \(\chi_{3006}(7, \cdot)\) | n/a | 27552 | 164 |
3006.2.p | \(\chi_{3006}(5, \cdot)\) | n/a | 27552 | 164 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3006))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1503))\)\(^{\oplus 2}\)