Defining parameters
Level: | \( N \) | \(=\) | \( 2007 = 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2007.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 223 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2007, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23 | 11 | 12 |
Cusp forms | 19 | 10 | 9 |
Eisenstein series | 4 | 1 | 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 \(S_{1}^{\mathrm{new}}(2007, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2007.1.d.a | $1$ | $1.002$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-223}) \) | \(\Q(\sqrt{669}) \) | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-q^{4}-2q^{7}+q^{16}+2q^{19}+q^{25}+\cdots\) |
2007.1.d.b | $3$ | $1.002$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-223}) \) | None | \(1\) | \(0\) | \(0\) | \(-1\) | \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\) |
2007.1.d.c | $6$ | $1.002$ | \(\Q(\zeta_{28})^+\) | $D_{14}$ | \(\Q(\sqrt{-223}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2007, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2007, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(223, [\chi])\)\(^{\oplus 3}\)