Defining parameters
Level: | \( N \) | \(=\) | \( 2000 = 2^{4} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2000.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(300\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 49 | 4 | 45 |
Cusp forms | 19 | 4 | 15 |
Eisenstein series | 30 | 0 | 30 |
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 \(S_{1}^{\mathrm{new}}(2000, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2000.1.h.a | $4$ | $0.998$ | \(\Q(\zeta_{20})^+\) | $D_{10}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+\beta _{3}q^{7}+(2+\beta _{2})q^{9}+(-1+\cdots)q^{21}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2000, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)