Defining parameters
Level: | \( N \) | = | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(237600\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1150))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80432 | 24240 | 56192 |
Cusp forms | 77968 | 24240 | 53728 |
Eisenstein series | 2464 | 0 | 2464 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1150))\)
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 |
---|---|---|---|---|
1150.3.c | \(\chi_{1150}(1149, \cdot)\) | 1150.3.c.a | 8 | 1 |
1150.3.c.b | 32 | |||
1150.3.c.c | 32 | |||
1150.3.d | \(\chi_{1150}(551, \cdot)\) | 1150.3.d.a | 4 | 1 |
1150.3.d.b | 16 | |||
1150.3.d.c | 16 | |||
1150.3.d.d | 16 | |||
1150.3.d.e | 24 | |||
1150.3.f | \(\chi_{1150}(93, \cdot)\) | n/a | 132 | 2 |
1150.3.h | \(\chi_{1150}(91, \cdot)\) | n/a | 480 | 4 |
1150.3.j | \(\chi_{1150}(229, \cdot)\) | n/a | 480 | 4 |
1150.3.l | \(\chi_{1150}(47, \cdot)\) | n/a | 880 | 8 |
1150.3.n | \(\chi_{1150}(51, \cdot)\) | n/a | 760 | 10 |
1150.3.o | \(\chi_{1150}(99, \cdot)\) | n/a | 720 | 10 |
1150.3.q | \(\chi_{1150}(193, \cdot)\) | n/a | 1440 | 20 |
1150.3.t | \(\chi_{1150}(19, \cdot)\) | n/a | 4800 | 40 |
1150.3.v | \(\chi_{1150}(11, \cdot)\) | n/a | 4800 | 40 |
1150.3.x | \(\chi_{1150}(3, \cdot)\) | n/a | 9600 | 80 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1150))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(1150)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 2}\)