Defining parameters
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.bt (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 315 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 8 | 36 |
Cusp forms | 20 | 8 | 12 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1260.1.bt.a | $2$ | $0.629$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(-1\) | \(-1\) | \(-1\) | \(q-\zeta_{6}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
1260.1.bt.b | $2$ | $0.629$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(-1\) | \(-1\) | \(-1\) | \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\) |
1260.1.bt.c | $2$ | $0.629$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(1\) | \(1\) | \(1\) | \(q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
1260.1.bt.d | $2$ | $0.629$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(1\) | \(1\) | \(1\) | \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)