Defining parameters
Level: | \( N \) | \(=\) | \( 1775 = 5^{2} \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1775.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 355 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1775, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 8 | 18 |
Cusp forms | 20 | 6 | 14 |
Eisenstein series | 6 | 2 | 4 |
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 \(S_{1}^{\mathrm{new}}(1775, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1775.1.c.a | $6$ | $0.886$ | 6.0.153664.1 | $D_{7}$ | \(\Q(\sqrt{-71}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1775, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1775, [\chi]) \cong \)