Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 24 | 184 |
Cusp forms | 176 | 24 | 152 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
384.4.d.a | $2$ | $22.657$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-24\) | \(q-3 i q^{3}+8 i q^{5}-12 q^{7}-9 q^{9}+\cdots\) |
384.4.d.b | $2$ | $22.657$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(24\) | \(q+3 i q^{3}+8 i q^{5}+12 q^{7}-9 q^{9}+\cdots\) |
384.4.d.c | $4$ | $22.657$ | \(\Q(i, \sqrt{13})\) | None | \(0\) | \(0\) | \(0\) | \(-32\) | \(q-3\beta _{1}q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+(-8+\cdots)q^{7}+\cdots\) |
384.4.d.d | $4$ | $22.657$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\beta_1 q^{3}+\beta_{2} q^{5}-5\beta_{3} q^{7}-9 q^{9}+\cdots\) |
384.4.d.e | $4$ | $22.657$ | \(\Q(i, \sqrt{13})\) | None | \(0\) | \(0\) | \(0\) | \(32\) | \(q+3\beta _{1}q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+(8-\beta _{3})q^{7}+\cdots\) |
384.4.d.f | $8$ | $22.657$ | 8.0.1534132224.8 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{7}-9q^{9}+(-4\beta _{1}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(384, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)