Defining parameters
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1003 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1003, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10 | 10 | 0 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 4 | 4 | 0 |
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 \(S_{1}^{\mathrm{new}}(1003, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1003.1.f.a | $2$ | $0.501$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(-2\) | \(-2\) | \(-2\) | \(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\) |
1003.1.f.b | $4$ | $0.501$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(2\) | \(2\) | \(2\) | \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\) |