Defining parameters
Level: | \( N \) | = | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 9 \) | ||
Sturm bound: | \(8640\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(152))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3708 | 2047 | 1661 |
Cusp forms | 3492 | 1979 | 1513 |
Eisenstein series | 216 | 68 | 148 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(152))\)
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 |
---|---|---|---|---|
152.6.a | \(\chi_{152}(1, \cdot)\) | 152.6.a.a | 1 | 1 |
152.6.a.b | 3 | |||
152.6.a.c | 6 | |||
152.6.a.d | 6 | |||
152.6.a.e | 7 | |||
152.6.b | \(\chi_{152}(75, \cdot)\) | 152.6.b.a | 2 | 1 |
152.6.b.b | 96 | |||
152.6.c | \(\chi_{152}(77, \cdot)\) | 152.6.c.a | 90 | 1 |
152.6.h | \(\chi_{152}(151, \cdot)\) | None | 0 | 1 |
152.6.i | \(\chi_{152}(49, \cdot)\) | 152.6.i.a | 24 | 2 |
152.6.i.b | 26 | |||
152.6.j | \(\chi_{152}(31, \cdot)\) | None | 0 | 2 |
152.6.o | \(\chi_{152}(27, \cdot)\) | n/a | 196 | 2 |
152.6.p | \(\chi_{152}(45, \cdot)\) | n/a | 196 | 2 |
152.6.q | \(\chi_{152}(9, \cdot)\) | n/a | 150 | 6 |
152.6.t | \(\chi_{152}(5, \cdot)\) | n/a | 588 | 6 |
152.6.v | \(\chi_{152}(3, \cdot)\) | n/a | 588 | 6 |
152.6.w | \(\chi_{152}(15, \cdot)\) | None | 0 | 6 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)