Defining parameters
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 88 | 296 |
Cusp forms | 288 | 72 | 216 |
Eisenstein series | 96 | 16 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
1323.2.o.a | \(2\) | \(10.564\) | \(\Q(\sqrt{-3}) \) | None | \(-3\) | \(0\) | \(-3\) | \(0\) | \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\) |
1323.2.o.b | \(2\) | \(10.564\) | \(\Q(\sqrt{-3}) \) | None | \(-3\) | \(0\) | \(3\) | \(0\) | \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\) |
1323.2.o.c | \(10\) | \(10.564\) | 10.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\) |
1323.2.o.d | \(10\) | \(10.564\) | 10.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\) |
1323.2.o.e | \(48\) | \(10.564\) | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)