Defining parameters
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cj (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 252 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1224 | 96 | 1128 |
Cusp forms | 1080 | 96 | 984 |
Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3024.2.cj.a | $2$ | $24.147$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(3\) | \(-4\) | \(q+(2-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\) |
3024.2.cj.b | $2$ | $24.147$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(3\) | \(4\) | \(q+(2-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\) |
3024.2.cj.c | $30$ | $24.147$ | None | \(0\) | \(0\) | \(-3\) | \(-7\) | ||
3024.2.cj.d | $30$ | $24.147$ | None | \(0\) | \(0\) | \(-3\) | \(7\) | ||
3024.2.cj.e | $32$ | $24.147$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)