Defining parameters
Level: | \( N \) | = | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(76032\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(690))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26048 | 5784 | 20264 |
Cusp forms | 24640 | 5784 | 18856 |
Eisenstein series | 1408 | 0 | 1408 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(690))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
690.3.b | \(\chi_{690}(599, \cdot)\) | 690.3.b.a | 88 | 1 |
690.3.c | \(\chi_{690}(91, \cdot)\) | 690.3.c.a | 32 | 1 |
690.3.f | \(\chi_{690}(229, \cdot)\) | 690.3.f.a | 48 | 1 |
690.3.g | \(\chi_{690}(461, \cdot)\) | 690.3.g.a | 56 | 1 |
690.3.k | \(\chi_{690}(277, \cdot)\) | 690.3.k.a | 40 | 2 |
690.3.k.b | 48 | |||
690.3.l | \(\chi_{690}(137, \cdot)\) | n/a | 192 | 2 |
690.3.o | \(\chi_{690}(41, \cdot)\) | n/a | 640 | 10 |
690.3.p | \(\chi_{690}(19, \cdot)\) | n/a | 480 | 10 |
690.3.s | \(\chi_{690}(61, \cdot)\) | n/a | 320 | 10 |
690.3.t | \(\chi_{690}(29, \cdot)\) | n/a | 960 | 10 |
690.3.u | \(\chi_{690}(17, \cdot)\) | n/a | 1920 | 20 |
690.3.v | \(\chi_{690}(13, \cdot)\) | n/a | 960 | 20 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(690))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(690)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 2}\)