Defining parameters
Level: | \( N \) | = | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(6912\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(140))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3000 | 1502 | 1498 |
Cusp forms | 2760 | 1446 | 1314 |
Eisenstein series | 240 | 56 | 184 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(140))\)
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 |
---|---|---|---|---|
140.6.a | \(\chi_{140}(1, \cdot)\) | 140.6.a.a | 2 | 1 |
140.6.a.b | 2 | |||
140.6.a.c | 3 | |||
140.6.a.d | 3 | |||
140.6.c | \(\chi_{140}(139, \cdot)\) | n/a | 116 | 1 |
140.6.e | \(\chi_{140}(29, \cdot)\) | 140.6.e.a | 16 | 1 |
140.6.g | \(\chi_{140}(111, \cdot)\) | 140.6.g.a | 80 | 1 |
140.6.i | \(\chi_{140}(81, \cdot)\) | 140.6.i.a | 2 | 2 |
140.6.i.b | 4 | |||
140.6.i.c | 8 | |||
140.6.i.d | 14 | |||
140.6.k | \(\chi_{140}(43, \cdot)\) | n/a | 180 | 2 |
140.6.m | \(\chi_{140}(13, \cdot)\) | 140.6.m.a | 40 | 2 |
140.6.o | \(\chi_{140}(31, \cdot)\) | n/a | 160 | 2 |
140.6.q | \(\chi_{140}(9, \cdot)\) | 140.6.q.a | 40 | 2 |
140.6.s | \(\chi_{140}(19, \cdot)\) | n/a | 232 | 2 |
140.6.u | \(\chi_{140}(17, \cdot)\) | 140.6.u.a | 80 | 4 |
140.6.w | \(\chi_{140}(23, \cdot)\) | n/a | 464 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(140)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)