Defining parameters
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.q (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 480 | 24 | 456 |
Cusp forms | 384 | 24 | 360 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1080.2.q.a | $2$ | $8.624$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-1\) | \(0\) | \(q-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{11}-3q^{17}+\cdots\) |
1080.2.q.b | $4$ | $8.624$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-2\) | \(-4\) | \(q+(-1+\zeta_{12})q^{5}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\) |
1080.2.q.c | $4$ | $8.624$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(-2\) | \(-2\) | \(q+(-1+\beta _{1})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+2q^{17}+\cdots\) |
1080.2.q.d | $6$ | $8.624$ | 6.0.954288.1 | None | \(0\) | \(0\) | \(3\) | \(5\) | \(q+\beta _{3}q^{5}+(1-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots\) |
1080.2.q.e | $8$ | $8.624$ | 8.0.856615824.2 | None | \(0\) | \(0\) | \(4\) | \(1\) | \(q+\beta _{1}q^{5}+\beta _{2}q^{7}+(-\beta _{2}+\beta _{6}-\beta _{7})q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)