Defining parameters
Level: | \( N \) | \(=\) | \( 5000 = 2^{3} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5000.k (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q(i)\) | ||
Sturm bound: | \(1500\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1560 | 992 | 568 |
Cusp forms | 1440 | 928 | 512 |
Eisenstein series | 120 | 64 | 56 |
Decomposition of \(S_{2}^{\mathrm{new}}(5000, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 2}\)