Properties

Label 2.0.67.1-323.4-a
Base field \(\Q(\sqrt{-67}) \)
Weight $2$
Level norm $323$
Level \( \left(2 a + 15\right) \)
Dimension $1$
CM no
Base change no
Sign $-1$
Analytic rank odd

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Base field: \(\Q(\sqrt{-67}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 17\); class number \(1\).

Form

Weight: 2
Level: 323.4 = \( \left(2 a + 15\right) \)
Level norm: 323
Dimension: 1
CM: no
Base change: no
Newspace:2.0.67.1-323.4 (dimension 1)
Sign of functional equation: $-1$
Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 17 \) 17.2 = \( \left(a - 1\right) \) \( -1 \)
\( 19 \) 19.2 = \( \left(a - 2\right) \) \( -1 \)

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 4 \) 4.1 = \( \left(2\right) \) \( 1 \)
\( 9 \) 9.1 = \( \left(3\right) \) \( 2 \)
\( 17 \) 17.1 = \( \left(-a\right) \) \( 2 \)
\( 19 \) 19.1 = \( \left(a + 1\right) \) \( 4 \)
\( 23 \) 23.1 = \( \left(a + 2\right) \) \( -4 \)
\( 23 \) 23.2 = \( \left(a - 3\right) \) \( 0 \)
\( 25 \) 25.1 = \( \left(5\right) \) \( 2 \)
\( 29 \) 29.1 = \( \left(a + 3\right) \) \( -2 \)
\( 29 \) 29.2 = \( \left(a - 4\right) \) \( 2 \)
\( 37 \) 37.1 = \( \left(a + 4\right) \) \( -6 \)
\( 37 \) 37.2 = \( \left(a - 5\right) \) \( -10 \)
\( 47 \) 47.1 = \( \left(a + 5\right) \) \( -4 \)
\( 47 \) 47.2 = \( \left(a - 6\right) \) \( 0 \)
\( 49 \) 49.1 = \( \left(7\right) \) \( -10 \)
\( 59 \) 59.1 = \( \left(a + 6\right) \) \( -12 \)
\( 59 \) 59.2 = \( \left(a - 7\right) \) \( -4 \)
\( 67 \) 67.1 = \( \left(-2 a + 1\right) \) \( 4 \)
\( 71 \) 71.1 = \( \left(-2 a + 3\right) \) \( 8 \)
\( 71 \) 71.2 = \( \left(2 a + 1\right) \) \( 4 \)
\( 73 \) 73.1 = \( \left(a + 7\right) \) \( -6 \)
Display number of eigenvalues