Defining parameters
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(150\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 4 | 14 |
Cusp forms | 8 | 4 | 4 |
Eisenstein series | 10 | 0 | 10 |
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 \(S_{1}^{\mathrm{new}}(1000, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1000.1.e.a | $2$ | $0.499$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-10}) \) | None | \(-2\) | \(0\) | \(0\) | \(1\) | \(q-q^{2}+q^{4}+(1-\beta )q^{7}-q^{8}+q^{9}+\cdots\) |
1000.1.e.b | $2$ | $0.499$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-10}) \) | None | \(2\) | \(0\) | \(0\) | \(-1\) | \(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1000, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)