Defining parameters
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(500\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1875, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 280 | 80 | 200 |
Cusp forms | 220 | 80 | 140 |
Eisenstein series | 60 | 0 | 60 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1875, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1875, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 2}\)