Defining parameters
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.h (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(190\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1805, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 38 | 8 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 40 | 32 | 8 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1805.1.h.a | $2$ | $0.901$ | \(\Q(\sqrt{-3}) \) | $D_{2}$ | \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(-1\) | \(0\) | \(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}-q^{11}+\cdots\) |
1805.1.h.b | $4$ | $0.901$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | $D_{4}$ | \(\Q(\sqrt{-95}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\) |