Defining parameters
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 57 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(342, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 188 | 20 | 168 |
Cusp forms | 172 | 20 | 152 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(342, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
342.4.b.a | $10$ | $20.179$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(-20\) | \(0\) | \(0\) | \(28\) | \(q-2q^{2}+4q^{4}+\beta _{5}q^{5}+(3+\beta _{3})q^{7}+\cdots\) |
342.4.b.b | $10$ | $20.179$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(20\) | \(0\) | \(0\) | \(28\) | \(q+2q^{2}+4q^{4}+\beta _{5}q^{5}+(3+\beta _{3})q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(342, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(342, [\chi]) \cong \)