Defining parameters
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(280\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(2\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(441, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 54 | 186 |
Cusp forms | 208 | 54 | 154 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(441, [\chi])\) into newform subspaces
Decomposition of \(S_{5}^{\mathrm{old}}(441, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)