Defining parameters
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(28, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 2 | 9 |
Cusp forms | 5 | 2 | 3 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(28, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
28.3.b.a | $2$ | $0.763$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(0\) | \(0\) | \(10\) | \(q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(28, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)