Defining parameters
Level: | \( N \) | \(=\) | \( 3888 = 2^{4} \cdot 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3888.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
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 | 86 | 5 | 81 |
Cusp forms | 32 | 5 | 27 |
Eisenstein series | 54 | 0 | 54 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 3 | 0 | 2 | 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.e.a | $1$ | $1.940$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-2q^{7}-q^{13}+q^{19}+q^{25}+q^{31}+\cdots\) |
3888.1.e.b | $1$ | $1.940$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(q+q^{7}-q^{13}+q^{19}+q^{25}+q^{31}+\cdots\) |
3888.1.e.c | $1$ | $1.940$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(q+q^{7}+2q^{13}-2q^{19}+q^{25}+q^{31}+\cdots\) |
3888.1.e.d | $2$ | $1.940$ | \(\Q(\sqrt{-2}) \) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{5}-\beta q^{11}+q^{13}-\beta q^{17}+q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3888, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3888, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1944, [\chi])\)\(^{\oplus 2}\)