Defining parameters
Level: | \( N \) | = | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(43200\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(300))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 19480 | 7779 | 11701 |
Cusp forms | 18920 | 7699 | 11221 |
Eisenstein series | 560 | 80 | 480 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(300))\)
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 |
---|---|---|---|---|
300.9.b | \(\chi_{300}(149, \cdot)\) | 300.9.b.a | 2 | 1 |
300.9.b.b | 2 | |||
300.9.b.c | 4 | |||
300.9.b.d | 20 | |||
300.9.b.e | 20 | |||
300.9.c | \(\chi_{300}(151, \cdot)\) | n/a | 152 | 1 |
300.9.f | \(\chi_{300}(199, \cdot)\) | n/a | 144 | 1 |
300.9.g | \(\chi_{300}(101, \cdot)\) | 300.9.g.a | 1 | 1 |
300.9.g.b | 1 | |||
300.9.g.c | 1 | |||
300.9.g.d | 2 | |||
300.9.g.e | 10 | |||
300.9.g.f | 10 | |||
300.9.g.g | 10 | |||
300.9.g.h | 16 | |||
300.9.k | \(\chi_{300}(157, \cdot)\) | 300.9.k.a | 4 | 2 |
300.9.k.b | 8 | |||
300.9.k.c | 8 | |||
300.9.k.d | 12 | |||
300.9.k.e | 16 | |||
300.9.l | \(\chi_{300}(107, \cdot)\) | n/a | 568 | 2 |
300.9.p | \(\chi_{300}(31, \cdot)\) | n/a | 960 | 4 |
300.9.q | \(\chi_{300}(29, \cdot)\) | n/a | 320 | 4 |
300.9.s | \(\chi_{300}(41, \cdot)\) | n/a | 320 | 4 |
300.9.t | \(\chi_{300}(19, \cdot)\) | n/a | 960 | 4 |
300.9.u | \(\chi_{300}(23, \cdot)\) | n/a | 3808 | 8 |
300.9.v | \(\chi_{300}(13, \cdot)\) | n/a | 320 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 1}\)