Defining parameters
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 138 | 13 | 125 |
Cusp forms | 102 | 13 | 89 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(300, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(300, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)