Defining parameters
Level: | \( N \) | = | \( 1849 = 43^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(1138984\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1849))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 428463 | 427960 | 503 |
Cusp forms | 425775 | 425355 | 420 |
Eisenstein series | 2688 | 2605 | 83 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1849))\)
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 |
---|---|---|---|---|
1849.4.a | \(\chi_{1849}(1, \cdot)\) | 1849.4.a.a | 1 | 1 |
1849.4.a.b | 4 | |||
1849.4.a.c | 6 | |||
1849.4.a.d | 10 | |||
1849.4.a.e | 10 | |||
1849.4.a.f | 10 | |||
1849.4.a.g | 30 | |||
1849.4.a.h | 30 | |||
1849.4.a.i | 50 | |||
1849.4.a.j | 50 | |||
1849.4.a.k | 60 | |||
1849.4.a.l | 60 | |||
1849.4.a.m | 110 | |||
1849.4.c | \(\chi_{1849}(423, \cdot)\) | n/a | 862 | 2 |
1849.4.e | \(\chi_{1849}(78, \cdot)\) | n/a | 2586 | 6 |
1849.4.g | \(\chi_{1849}(210, \cdot)\) | n/a | 5172 | 12 |
1849.4.i | \(\chi_{1849}(44, \cdot)\) | n/a | 19824 | 42 |
1849.4.k | \(\chi_{1849}(6, \cdot)\) | n/a | 39648 | 84 |
1849.4.m | \(\chi_{1849}(4, \cdot)\) | n/a | 118944 | 252 |
1849.4.o | \(\chi_{1849}(9, \cdot)\) | n/a | 237888 | 504 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1849))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1849)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)