Defining parameters
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.u (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 64 | 200 |
Cusp forms | 216 | 56 | 160 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)