Defining parameters
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(182\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1859, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 21 | 3 |
Cusp forms | 10 | 10 | 0 |
Eisenstein series | 14 | 11 | 3 |
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 \(S_{1}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1859.1.c.a | $3$ | $0.928$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\) |
1859.1.c.b | $3$ | $0.928$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(-1\) | \(1\) | \(0\) | \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\) |
1859.1.c.c | $4$ | $0.928$ | \(\Q(i, \sqrt{5})\) | $D_{5}$ | \(\Q(\sqrt{-143}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots\) |