Defining parameters
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.bf (of order \(28\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2001 \) |
Character field: | \(\Q(\zeta_{28})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2001, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 120 | 0 |
Cusp forms | 72 | 72 | 0 |
Eisenstein series | 48 | 48 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 72 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2001, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2001.1.bf.a | $12$ | $0.999$ | \(\Q(\zeta_{28})\) | $D_{28}$ | \(\Q(\sqrt{-23}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots\) |
2001.1.bf.b | $12$ | $0.999$ | \(\Q(\zeta_{28})\) | $D_{28}$ | \(\Q(\sqrt{-23}) \) | None | \(2\) | \(-2\) | \(0\) | \(0\) | \(q+(\zeta_{28}^{7}+\zeta_{28}^{10})q^{2}-\zeta_{28}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\) |
2001.1.bf.c | $24$ | $0.999$ | \(\Q(\zeta_{84})\) | $D_{84}$ | \(\Q(\sqrt{-23}) \) | None | \(-2\) | \(2\) | \(0\) | \(0\) | \(q+(-\zeta_{84}^{7}-\zeta_{84}^{20})q^{2}-\zeta_{84}^{26}q^{3}+\cdots\) |
2001.1.bf.d | $24$ | $0.999$ | \(\Q(\zeta_{84})\) | $D_{84}$ | \(\Q(\sqrt{-23}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{84}^{7}+\zeta_{84}^{20})q^{2}+\zeta_{84}^{25}q^{3}+\cdots\) |