Defining parameters
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.bf (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 456 | 96 | 360 |
Cusp forms | 408 | 96 | 312 |
Eisenstein series | 48 | 0 | 48 |
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.bf.a | $4$ | $8.624$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(0\) | \(8\) | \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots\) |
1080.2.bf.b | $92$ | $8.624$ | None | \(-2\) | \(0\) | \(0\) | \(-8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)