Defining parameters
Level: | \( N \) | = | \( 1849 = 43^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(569492\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1849))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 143717 | 143521 | 196 |
Cusp forms | 141030 | 140916 | 114 |
Eisenstein series | 2687 | 2605 | 82 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1849))\)
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 |
---|---|---|---|---|
1849.2.a | \(\chi_{1849}(1, \cdot)\) | 1849.2.a.a | 1 | 1 |
1849.2.a.b | 1 | |||
1849.2.a.c | 1 | |||
1849.2.a.d | 1 | |||
1849.2.a.e | 2 | |||
1849.2.a.f | 2 | |||
1849.2.a.g | 2 | |||
1849.2.a.h | 2 | |||
1849.2.a.i | 3 | |||
1849.2.a.j | 3 | |||
1849.2.a.k | 3 | |||
1849.2.a.l | 3 | |||
1849.2.a.m | 10 | |||
1849.2.a.n | 18 | |||
1849.2.a.o | 18 | |||
1849.2.a.p | 20 | |||
1849.2.a.q | 20 | |||
1849.2.a.r | 20 | |||
1849.2.c | \(\chi_{1849}(423, \cdot)\) | n/a | 260 | 2 |
1849.2.e | \(\chi_{1849}(78, \cdot)\) | n/a | 786 | 6 |
1849.2.g | \(\chi_{1849}(210, \cdot)\) | n/a | 1560 | 12 |
1849.2.i | \(\chi_{1849}(44, \cdot)\) | n/a | 6552 | 42 |
1849.2.k | \(\chi_{1849}(6, \cdot)\) | n/a | 13188 | 84 |
1849.2.m | \(\chi_{1849}(4, \cdot)\) | n/a | 39312 | 252 |
1849.2.o | \(\chi_{1849}(9, \cdot)\) | n/a | 79128 | 504 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1849))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1849)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)