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: | \(\Q\) | ||
Newforms: | \( 1 \) | ||
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 irreducible Hecke orbits
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
\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)