Defining parameters
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(378, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 168 | 16 | 152 |
Cusp forms | 120 | 16 | 104 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
378.2.e.a | $2$ | $3.018$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(-3\) | \(-4\) | \(q-q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\) |
378.2.e.b | $2$ | $3.018$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(3\) | \(-4\) | \(q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\) |
378.2.e.c | $6$ | $3.018$ | 6.0.309123.1 | None | \(-6\) | \(0\) | \(5\) | \(4\) | \(q-q^{2}+q^{4}+(2-2\beta _{4}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\) |
378.2.e.d | $6$ | $3.018$ | 6.0.309123.1 | None | \(6\) | \(0\) | \(-1\) | \(2\) | \(q+q^{2}+q^{4}-\beta _{2}q^{5}+(\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(378, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)