Base field: \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 1\); class number \(1\).
Form
| Weight: | 2 | |
| Level: | 97344.2 = \( \left(312\right) \) | |
| Level norm: | 97344 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.3.1-97344.2 (dimension 17) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | odd |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(a + 1\right) \) | \( -1 \) |
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( 1 \) |
| \( 13 \) | 13.1 = \( \left(a + 3\right) \) | \( 1 \) |
| \( 13 \) | 13.2 = \( \left(a - 4\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 7 \) | 7.1 = \( \left(-a - 2\right) \) | \( -2 \) |
| \( 7 \) | 7.2 = \( \left(a - 3\right) \) | \( 0 \) |
| \( 19 \) | 19.1 = \( \left(-2 a + 5\right) \) | \( 4 \) |
| \( 19 \) | 19.2 = \( \left(2 a + 3\right) \) | \( -6 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( 6 \) |
| \( 31 \) | 31.1 = \( \left(a + 5\right) \) | \( -2 \) |
| \( 31 \) | 31.2 = \( \left(a - 6\right) \) | \( 4 \) |
| \( 37 \) | 37.1 = \( \left(-3 a + 7\right) \) | \( 8 \) |
| \( 37 \) | 37.2 = \( \left(3 a + 4\right) \) | \( 0 \) |
| \( 43 \) | 43.1 = \( \left(a + 6\right) \) | \( -4 \) |
| \( 43 \) | 43.2 = \( \left(a - 7\right) \) | \( -12 \) |
| \( 61 \) | 61.1 = \( \left(-4 a + 9\right) \) | \( 10 \) |
| \( 61 \) | 61.2 = \( \left(4 a + 5\right) \) | \( -14 \) |
| \( 67 \) | 67.1 = \( \left(-2 a + 9\right) \) | \( 2 \) |
| \( 67 \) | 67.2 = \( \left(2 a + 7\right) \) | \( -4 \) |
| \( 73 \) | 73.1 = \( \left(a + 8\right) \) | \( 12 \) |
| \( 73 \) | 73.2 = \( \left(a - 9\right) \) | \( 0 \) |
| \( 79 \) | 79.1 = \( \left(-3 a + 10\right) \) | \( -12 \) |
| \( 79 \) | 79.2 = \( \left(3 a + 7\right) \) | \( 0 \) |
| \( 97 \) | 97.1 = \( \left(-3 a - 8\right) \) | \( 4 \) |