Defining parameters
Level: | \( N \) | = | \( 2230 = 2 \cdot 5 \cdot 223 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(596736\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2230))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 150960 | 45585 | 105375 |
Cusp forms | 147409 | 45585 | 101824 |
Eisenstein series | 3551 | 0 | 3551 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2230))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
2230.2.a | \(\chi_{2230}(1, \cdot)\) | 2230.2.a.a | 1 | 1 |
2230.2.a.b | 1 | |||
2230.2.a.c | 1 | |||
2230.2.a.d | 1 | |||
2230.2.a.e | 1 | |||
2230.2.a.f | 1 | |||
2230.2.a.g | 2 | |||
2230.2.a.h | 2 | |||
2230.2.a.i | 2 | |||
2230.2.a.j | 2 | |||
2230.2.a.k | 2 | |||
2230.2.a.l | 3 | |||
2230.2.a.m | 4 | |||
2230.2.a.n | 4 | |||
2230.2.a.o | 5 | |||
2230.2.a.p | 6 | |||
2230.2.a.q | 7 | |||
2230.2.a.r | 7 | |||
2230.2.a.s | 10 | |||
2230.2.a.t | 11 | |||
2230.2.b | \(\chi_{2230}(1339, \cdot)\) | n/a | 112 | 1 |
2230.2.e | \(\chi_{2230}(931, \cdot)\) | n/a | 152 | 2 |
2230.2.f | \(\chi_{2230}(1337, \cdot)\) | n/a | 224 | 2 |
2230.2.i | \(\chi_{2230}(39, \cdot)\) | n/a | 224 | 2 |
2230.2.l | \(\chi_{2230}(263, \cdot)\) | n/a | 448 | 4 |
2230.2.m | \(\chi_{2230}(41, \cdot)\) | n/a | 2592 | 36 |
2230.2.p | \(\chi_{2230}(49, \cdot)\) | n/a | 4032 | 36 |
2230.2.q | \(\chi_{2230}(31, \cdot)\) | n/a | 5472 | 72 |
2230.2.s | \(\chi_{2230}(13, \cdot)\) | n/a | 8064 | 72 |
2230.2.u | \(\chi_{2230}(9, \cdot)\) | n/a | 8064 | 72 |
2230.2.w | \(\chi_{2230}(3, \cdot)\) | n/a | 16128 | 144 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2230))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2230)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2230))\)\(^{\oplus 1}\)