Defining parameters
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1003 \) |
Character field: | \(\Q\) | ||
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 | 5 | 5 | 0 |
Cusp forms | 3 | 3 | 0 |
Eisenstein series | 2 | 2 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 3 | 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.b.a | $1$ | $0.501$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \) | \(\Q(\sqrt{17}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\) |
1003.1.b.b | $2$ | $0.501$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\) |