Defining parameters
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.q (of order \(15\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 77 \) |
Character field: | \(\Q(\zeta_{15})\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(539, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 512 | 352 | 160 |
Cusp forms | 384 | 288 | 96 |
Eisenstein series | 128 | 64 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(539, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(539, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(539, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)