Defining parameters
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 36 | 96 |
Cusp forms | 108 | 36 | 72 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(600, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)