Defining parameters
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(46\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(49, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 92 | 64 | 28 |
Cusp forms | 76 | 56 | 20 |
Eisenstein series | 16 | 8 | 8 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(49, [\chi])\) into newform subspaces
Decomposition of \(S_{10}^{\mathrm{old}}(49, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(49, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)