Defining parameters
Level: | \( N \) | \(=\) | \( 1352 = 2^{3} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1352.p (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(182\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1352, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 36 | 8 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 28 | 20 | 8 |
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 \(S_{1}^{\mathrm{new}}(1352, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1352.1.p.a | $2$ | $0.675$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-26}) \) | None | \(-1\) | \(1\) | \(-2\) | \(1\) | \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots\) |
1352.1.p.b | $2$ | $0.675$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-26}) \) | None | \(1\) | \(1\) | \(2\) | \(-1\) | \(q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots\) |
1352.1.p.c | $12$ | $0.675$ | 12.0.\(\cdots\).1 | $D_{7}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+\beta _{11}q^{6}+\cdots\) |