Defining parameters
Level: | \( N \) | \(=\) | \( 1328 = 2^{4} \cdot 83 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1328.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 83 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1328, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 5 | 19 |
Cusp forms | 18 | 4 | 14 |
Eisenstein series | 6 | 1 | 5 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1328, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1328.1.g.a | $1$ | $0.663$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-83}) \) | None | \(0\) | \(1\) | \(0\) | \(1\) | \(q+q^{3}+q^{7}+q^{11}-q^{17}+q^{21}-2q^{23}+\cdots\) |
1328.1.g.b | $3$ | $0.663$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-83}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1328, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1328, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(83, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(332, [\chi])\)\(^{\oplus 3}\)