Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.bk (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(6\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 22 | 18 |
Cusp forms | 16 | 10 | 6 |
Eisenstein series | 24 | 12 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 10 | 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.bk.a | $2$ | $0.898$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(-1\) | \(-1\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}+q^{8}+\cdots\) |
1800.1.bk.b | $2$ | $0.898$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(-1\) | \(2\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\) |
1800.1.bk.c | $2$ | $0.898$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(1\) | \(-2\) | \(0\) | \(0\) | \(q-\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\) |
1800.1.bk.d | $2$ | $0.898$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(1\) | \(1\) | \(0\) | \(0\) | \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\) |
1800.1.bk.e | $2$ | $0.898$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(1\) | \(1\) | \(0\) | \(0\) | \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}-q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)