Defining parameters
Level: | \( N \) | \(=\) | \( 3888 = 2^{4} \cdot 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3888.q (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(648\) | ||
Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3888, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 164 | 10 | 154 |
Cusp forms | 56 | 10 | 46 |
Eisenstein series | 108 | 0 | 108 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3888, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3888.1.q.a | $2$ | $1.940$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-1\) | \(q+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots\) |
3888.1.q.b | $2$ | $1.940$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-1\) | \(q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\) |
3888.1.q.c | $2$ | $1.940$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\) |
3888.1.q.d | $4$ | $1.940$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3888, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3888, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1944, [\chi])\)\(^{\oplus 2}\)