Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
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: | \(128\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(11\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 16 | 64 |
Cusp forms | 48 | 16 | 32 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
384.2.c.a | $4$ | $3.066$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
384.2.c.b | $4$ | $3.066$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+(-1+\beta _{3})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\) |
384.2.c.c | $4$ | $3.066$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\) |
384.2.c.d | $4$ | $3.066$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(384, [\chi]) \cong \)