Defining parameters
Level: | \( N \) | \(=\) | \( 2816 = 2^{8} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2816.v (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 44 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2816, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 32 | 80 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 96 | 16 | 80 |
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 \(S_{1}^{\mathrm{new}}(2816, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2816.1.v.a | $4$ | $1.405$ | \(\Q(\zeta_{10})\) | $D_{10}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{10}+\zeta_{10}^{3})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots\) |
2816.1.v.b | $4$ | $1.405$ | \(\Q(\zeta_{10})\) | $D_{10}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{10}-\zeta_{10}^{3})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots\) |
2816.1.v.c | $8$ | $1.405$ | \(\Q(\zeta_{20})\) | $D_{5}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{20}-\zeta_{20}^{7})q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{9}+\cdots\) |