Defining parameters
Level: | \( N \) | \(=\) | \( 6400 = 2^{8} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6400.bx (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Sturm bound: | \(1920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7872 | 1952 | 5920 |
Cusp forms | 7488 | 1888 | 5600 |
Eisenstein series | 384 | 64 | 320 |
Decomposition of \(S_{2}^{\mathrm{new}}(6400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3200, [\chi])\)\(^{\oplus 2}\)