Defining parameters
Level: | \( N \) | \(=\) | \( 3136 = 2^{6} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3136.n (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(448\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3136, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 124 | 16 | 108 |
Cusp forms | 28 | 16 | 12 |
Eisenstein series | 96 | 0 | 96 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3136.1.n.a | $16$ | $1.565$ | \(\Q(\zeta_{48})\) | $D_{8}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{48}^{17}-\zeta_{48}^{23})q^{3}+(-\zeta_{48}^{10}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3136, [\chi]) \cong \)