Defining parameters
Level: | \( N \) | = | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 6 \) | ||
Sturm bound: | \(7200\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(150))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3112 | 691 | 2421 |
Cusp forms | 2888 | 691 | 2197 |
Eisenstein series | 224 | 0 | 224 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(150))\)
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 |
---|---|---|---|---|
150.6.a | \(\chi_{150}(1, \cdot)\) | 150.6.a.a | 1 | 1 |
150.6.a.b | 1 | |||
150.6.a.c | 1 | |||
150.6.a.d | 1 | |||
150.6.a.e | 1 | |||
150.6.a.f | 1 | |||
150.6.a.g | 1 | |||
150.6.a.h | 1 | |||
150.6.a.i | 1 | |||
150.6.a.j | 1 | |||
150.6.a.k | 1 | |||
150.6.a.l | 1 | |||
150.6.a.m | 1 | |||
150.6.a.n | 2 | |||
150.6.a.o | 2 | |||
150.6.c | \(\chi_{150}(49, \cdot)\) | 150.6.c.a | 2 | 1 |
150.6.c.b | 2 | |||
150.6.c.c | 2 | |||
150.6.c.d | 2 | |||
150.6.c.e | 2 | |||
150.6.c.f | 2 | |||
150.6.c.g | 2 | |||
150.6.e | \(\chi_{150}(107, \cdot)\) | 150.6.e.a | 16 | 2 |
150.6.e.b | 20 | |||
150.6.e.c | 24 | |||
150.6.g | \(\chi_{150}(31, \cdot)\) | 150.6.g.a | 20 | 4 |
150.6.g.b | 24 | |||
150.6.g.c | 24 | |||
150.6.g.d | 28 | |||
150.6.h | \(\chi_{150}(19, \cdot)\) | n/a | 104 | 4 |
150.6.l | \(\chi_{150}(17, \cdot)\) | n/a | 400 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)