Defining parameters
Level: | \( N \) | \(=\) | \( 3520 = 2^{6} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3520.y (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 220 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3520, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 20 | 76 |
Cusp forms | 48 | 12 | 36 |
Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3520.1.y.a | $2$ | $1.757$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+(-1-i)q^{3}+iq^{5}+iq^{9}-iq^{11}+\cdots\) |
3520.1.y.b | $2$ | $1.757$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(1+i)q^{3}+iq^{5}+iq^{9}+iq^{11}+\cdots\) |
3520.1.y.c | $4$ | $1.757$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+(\zeta_{12}^{4}-\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\) |
3520.1.y.d | $4$ | $1.757$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(-\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)