Defining parameters
Level: | \( N \) | = | \( 536 = 2^{3} \cdot 67 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(17952\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(536))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 436 | 168 | 268 |
Cusp forms | 40 | 38 | 2 |
Eisenstein series | 396 | 130 | 266 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 38 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(536))\)
We only show spaces with odd 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 |
---|---|---|---|---|
536.1.b | \(\chi_{536}(401, \cdot)\) | None | 0 | 1 |
536.1.d | \(\chi_{536}(135, \cdot)\) | None | 0 | 1 |
536.1.f | \(\chi_{536}(403, \cdot)\) | None | 0 | 1 |
536.1.h | \(\chi_{536}(133, \cdot)\) | 536.1.h.a | 3 | 1 |
536.1.h.b | 3 | |||
536.1.k | \(\chi_{536}(97, \cdot)\) | None | 0 | 2 |
536.1.m | \(\chi_{536}(431, \cdot)\) | None | 0 | 2 |
536.1.o | \(\chi_{536}(163, \cdot)\) | 536.1.o.a | 2 | 2 |
536.1.p | \(\chi_{536}(365, \cdot)\) | None | 0 | 2 |
536.1.r | \(\chi_{536}(5, \cdot)\) | None | 0 | 10 |
536.1.t | \(\chi_{536}(59, \cdot)\) | 536.1.t.a | 10 | 10 |
536.1.v | \(\chi_{536}(15, \cdot)\) | None | 0 | 10 |
536.1.x | \(\chi_{536}(137, \cdot)\) | None | 0 | 10 |
536.1.z | \(\chi_{536}(13, \cdot)\) | None | 0 | 20 |
536.1.ba | \(\chi_{536}(19, \cdot)\) | 536.1.ba.a | 20 | 20 |
536.1.bc | \(\chi_{536}(23, \cdot)\) | None | 0 | 20 |
536.1.be | \(\chi_{536}(41, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(536))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(536)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)