Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 48 | 160 |
Cusp forms | 176 | 48 | 128 |
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.c.a | $12$ | $22.657$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(-10\) | \(0\) | \(0\) | \(q+(-1+\beta _{5})q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\) |
384.4.c.b | $12$ | $22.657$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(-10\) | \(0\) | \(0\) | \(q+(-1+\beta _{6})q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\) |
384.4.c.c | $12$ | $22.657$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(10\) | \(0\) | \(0\) | \(q+(1-\beta _{6})q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\) |
384.4.c.d | $12$ | $22.657$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(10\) | \(0\) | \(0\) | \(q+(1-\beta _{5})q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(384, [\chi]) \cong \)