Defining parameters
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 17 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(450, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 474 | 38 | 436 |
Cusp forms | 426 | 38 | 388 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(450, [\chi])\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(450, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)