Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 288 | 72 | 216 |
Cusp forms | 224 | 56 | 168 |
Eisenstein series | 64 | 16 | 48 |
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.i.a | $8$ | $10.463$ | 8.0.629407744.1 | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}-\beta _{7})q^{5}+\cdots\) |
384.3.i.b | $8$ | $10.463$ | 8.0.629407744.1 | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\) |
384.3.i.c | $20$ | $10.463$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q-\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots\) |
384.3.i.d | $20$ | $10.463$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(6\) | \(0\) | \(0\) | \(q+\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}+\beta _{6}q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)