Defining parameters
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 82 | 6 | 76 |
Cusp forms | 34 | 6 | 28 |
Eisenstein series | 48 | 0 | 48 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3200.1.e.a | $2$ | $1.597$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+q^{9}-iq^{17}+q^{41}-q^{49}+iq^{73}+\cdots\) |
3200.1.e.b | $4$ | $1.597$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3200, [\chi]) \cong \)