Defining parameters
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(322, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 104 | 32 | 72 |
Cusp forms | 88 | 32 | 56 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(322, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
322.2.e.a | $8$ | $2.571$ | 8.0.310217769.2 | None | \(-4\) | \(-3\) | \(-7\) | \(-1\) | \(q+(-1+\beta _{5})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\) |
322.2.e.b | $8$ | $2.571$ | 8.0.1767277521.3 | None | \(-4\) | \(5\) | \(5\) | \(1\) | \(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\) |
322.2.e.c | $8$ | $2.571$ | 8.0.1767277521.3 | None | \(4\) | \(-1\) | \(-3\) | \(-1\) | \(q+(1-\beta _{6})q^{2}+(\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7})q^{3}+\cdots\) |
322.2.e.d | $8$ | $2.571$ | 8.0.6498455769.2 | None | \(4\) | \(-1\) | \(5\) | \(-3\) | \(q+(1-\beta _{5})q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(322, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)