Defining parameters
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(3456\) | ||
Trace bound: | \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6930, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1760 | 96 | 1664 |
Cusp forms | 1696 | 96 | 1600 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(6930, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
6930.2.g.a | $24$ | $55.336$ | None | \(-24\) | \(0\) | \(0\) | \(0\) | ||
6930.2.g.b | $24$ | $55.336$ | None | \(-24\) | \(0\) | \(0\) | \(0\) | ||
6930.2.g.c | $24$ | $55.336$ | None | \(24\) | \(0\) | \(0\) | \(0\) | ||
6930.2.g.d | $24$ | $55.336$ | None | \(24\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(6930, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6930, [\chi]) \cong \)