Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 16 | 128 |
Cusp forms | 112 | 16 | 96 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
384.3.g.a | $8$ | $10.463$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(-16\) | \(0\) | \(q-\zeta_{24}q^{3}+(-2+\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\) |
384.3.g.b | $8$ | $10.463$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(16\) | \(0\) | \(q+\zeta_{24}q^{3}+(2-\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)