Defining parameters
| Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(72\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 108 | 26 | 82 |
| Cusp forms | 84 | 22 | 62 |
| Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 144.3.q.a | \(2\) | \(3.924\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(3\) | \(6\) | \(2\) | \(q+(3-3\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-2\zeta_{6})q^{7}+\cdots\) |
| 144.3.q.b | \(4\) | \(3.924\) | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(0\) | \(-3\) | \(9\) | \(1\) | \(q+(-1+\beta _{3})q^{3}+(4-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\) |
| 144.3.q.c | \(4\) | \(3.924\) | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(-18\) | \(-2\) | \(q+(1-2\beta _{1}-\beta _{3})q^{3}+(-3-3\beta _{1})q^{5}+\cdots\) |
| 144.3.q.d | \(4\) | \(3.924\) | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(12\) | \(6\) | \(6\) | \(q+3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\) |
| 144.3.q.e | \(8\) | \(3.924\) | 8.0.\(\cdots\).9 | None | \(0\) | \(-10\) | \(-6\) | \(-6\) | \(q+(-1+\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)