Defining parameters
Level: | \( N \) | \(=\) | \( 540 = 2^{2} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 540.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(540, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 8 | 244 |
Cusp forms | 180 | 8 | 172 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(540, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
540.2.i.a | $2$ | $4.312$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(1\) | \(1\) | \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+4\zeta_{6}q^{13}+6q^{17}+\cdots\) |
540.2.i.b | $6$ | $4.312$ | 6.0.954288.1 | None | \(0\) | \(0\) | \(-3\) | \(-3\) | \(q+(-1-\beta _{2})q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(540, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)