Defining parameters
Level: | \( N \) | \(=\) | \( 1648 = 2^{4} \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1648.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 103 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(208\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1648, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 3 | 15 |
Cusp forms | 12 | 2 | 10 |
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 | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1648, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1648.1.c.a | $2$ | $0.822$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-103}) \) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(q+(1-\beta )q^{7}+q^{9}-\beta q^{13}+(-1+\beta )q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1648, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1648, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(206, [\chi])\)\(^{\oplus 4}\)