Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 7 | 27 |
Cusp forms | 10 | 4 | 6 |
Eisenstein series | 24 | 3 | 21 |
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 \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1800.1.g.a | $1$ | $0.898$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(-1\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\) |
1800.1.g.b | $1$ | $0.898$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(1\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+q^{4}+q^{8}+q^{11}+q^{16}-q^{17}+\cdots\) |
1800.1.g.c | $2$ | $0.898$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) | \(\Q(\sqrt{6}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \)