Defining parameters
Level: | \( N \) | = | \( 639 = 3^{2} \cdot 71 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(30240\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(639))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 586 | 328 | 258 |
Cusp forms | 26 | 17 | 9 |
Eisenstein series | 560 | 311 | 249 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 17 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(639))\)
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 |
---|---|---|---|---|
639.1.c | \(\chi_{639}(143, \cdot)\) | None | 0 | 1 |
639.1.d | \(\chi_{639}(496, \cdot)\) | 639.1.d.a | 3 | 1 |
639.1.g | \(\chi_{639}(70, \cdot)\) | 639.1.g.a | 2 | 2 |
639.1.g.b | 12 | |||
639.1.h | \(\chi_{639}(356, \cdot)\) | None | 0 | 2 |
639.1.k | \(\chi_{639}(46, \cdot)\) | None | 0 | 4 |
639.1.l | \(\chi_{639}(125, \cdot)\) | None | 0 | 4 |
639.1.n | \(\chi_{639}(181, \cdot)\) | None | 0 | 6 |
639.1.o | \(\chi_{639}(116, \cdot)\) | None | 0 | 6 |
639.1.t | \(\chi_{639}(5, \cdot)\) | None | 0 | 8 |
639.1.u | \(\chi_{639}(85, \cdot)\) | None | 0 | 8 |
639.1.x | \(\chi_{639}(20, \cdot)\) | None | 0 | 12 |
639.1.y | \(\chi_{639}(34, \cdot)\) | None | 0 | 12 |
639.1.ba | \(\chi_{639}(8, \cdot)\) | None | 0 | 24 |
639.1.bb | \(\chi_{639}(28, \cdot)\) | None | 0 | 24 |
639.1.bd | \(\chi_{639}(7, \cdot)\) | None | 0 | 48 |
639.1.be | \(\chi_{639}(2, \cdot)\) | None | 0 | 48 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(639))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(639)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 3}\)