Defining parameters
Level: | \( N \) | = | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(8640\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(126))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3984 | 982 | 3002 |
Cusp forms | 3792 | 982 | 2810 |
Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(126))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
126.10.a | \(\chi_{126}(1, \cdot)\) | 126.10.a.a | 1 | 1 |
126.10.a.b | 1 | |||
126.10.a.c | 1 | |||
126.10.a.d | 1 | |||
126.10.a.e | 1 | |||
126.10.a.f | 1 | |||
126.10.a.g | 1 | |||
126.10.a.h | 1 | |||
126.10.a.i | 2 | |||
126.10.a.j | 2 | |||
126.10.a.k | 2 | |||
126.10.a.l | 2 | |||
126.10.a.m | 2 | |||
126.10.a.n | 2 | |||
126.10.a.o | 2 | |||
126.10.d | \(\chi_{126}(125, \cdot)\) | 126.10.d.a | 24 | 1 |
126.10.e | \(\chi_{126}(25, \cdot)\) | n/a | 144 | 2 |
126.10.f | \(\chi_{126}(43, \cdot)\) | n/a | 108 | 2 |
126.10.g | \(\chi_{126}(37, \cdot)\) | 126.10.g.a | 2 | 2 |
126.10.g.b | 4 | |||
126.10.g.c | 4 | |||
126.10.g.d | 6 | |||
126.10.g.e | 6 | |||
126.10.g.f | 6 | |||
126.10.g.g | 8 | |||
126.10.g.h | 12 | |||
126.10.g.i | 12 | |||
126.10.h | \(\chi_{126}(67, \cdot)\) | n/a | 144 | 2 |
126.10.k | \(\chi_{126}(17, \cdot)\) | 126.10.k.a | 48 | 2 |
126.10.l | \(\chi_{126}(5, \cdot)\) | n/a | 144 | 2 |
126.10.m | \(\chi_{126}(41, \cdot)\) | n/a | 144 | 2 |
126.10.t | \(\chi_{126}(47, \cdot)\) | n/a | 144 | 2 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)