Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.cr (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 32 | 48 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 64 | 16 | 48 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1800.1.cr.a | $16$ | $0.898$ | \(\Q(\zeta_{40})\) | $D_{20}$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\zeta_{40}^{19}q^{2}-\zeta_{40}^{18}q^{4}+\zeta_{40}^{9}q^{5}+\cdots\) |