Defining parameters
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(14\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 408 | 72 | 336 |
Cusp forms | 312 | 72 | 240 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)