Defining parameters
Level: | \( N \) | = | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 18 \) | ||
Sturm bound: | \(162000\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(950))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 55008 | 16498 | 38510 |
Cusp forms | 52992 | 16498 | 36494 |
Eisenstein series | 2016 | 0 | 2016 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(950))\)
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 |
---|---|---|---|---|
950.3.c | \(\chi_{950}(151, \cdot)\) | 950.3.c.a | 2 | 1 |
950.3.c.b | 12 | |||
950.3.c.c | 12 | |||
950.3.c.d | 16 | |||
950.3.c.e | 20 | |||
950.3.d | \(\chi_{950}(949, \cdot)\) | 950.3.d.a | 4 | 1 |
950.3.d.b | 24 | |||
950.3.d.c | 32 | |||
950.3.g | \(\chi_{950}(343, \cdot)\) | n/a | 108 | 2 |
950.3.i | \(\chi_{950}(449, \cdot)\) | n/a | 120 | 2 |
950.3.k | \(\chi_{950}(601, \cdot)\) | n/a | 124 | 2 |
950.3.m | \(\chi_{950}(189, \cdot)\) | n/a | 400 | 4 |
950.3.o | \(\chi_{950}(341, \cdot)\) | n/a | 400 | 4 |
950.3.p | \(\chi_{950}(7, \cdot)\) | n/a | 240 | 4 |
950.3.s | \(\chi_{950}(51, \cdot)\) | n/a | 384 | 6 |
950.3.t | \(\chi_{950}(249, \cdot)\) | n/a | 360 | 6 |
950.3.v | \(\chi_{950}(77, \cdot)\) | n/a | 720 | 8 |
950.3.y | \(\chi_{950}(31, \cdot)\) | n/a | 800 | 8 |
950.3.z | \(\chi_{950}(69, \cdot)\) | n/a | 800 | 8 |
950.3.ba | \(\chi_{950}(43, \cdot)\) | n/a | 720 | 12 |
950.3.be | \(\chi_{950}(83, \cdot)\) | n/a | 1600 | 16 |
950.3.bf | \(\chi_{950}(21, \cdot)\) | n/a | 2400 | 24 |
950.3.bh | \(\chi_{950}(29, \cdot)\) | n/a | 2400 | 24 |
950.3.bj | \(\chi_{950}(17, \cdot)\) | n/a | 4800 | 48 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(950))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(950)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 2}\)