Defining parameters
Level: | \( N \) | \(=\) | \( 348 = 2^{2} \cdot 3 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 348.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 348 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(348, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 64 | 0 |
Cusp forms | 56 | 56 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(348, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
348.2.b.a | $8$ | $2.779$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\) |
348.2.b.b | $12$ | $2.779$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | \(\Q(\sqrt{-29}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{11}q^{3}-2q^{4}+\beta _{9}q^{5}+\cdots\) |
348.2.b.c | $12$ | $2.779$ | 12.0.\(\cdots\).3 | \(\Q(\sqrt{-87}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{6}q^{2}+\beta _{4}q^{3}+\beta _{5}q^{4}-\beta _{3}q^{6}+\cdots\) |
348.2.b.d | $24$ | $2.779$ | None | \(0\) | \(0\) | \(0\) | \(0\) |