Properties

Label 2.0.11.1-1764.2-a
Base field \(\Q(\sqrt{-11}) \)
Weight $2$
Level norm $1764$
Level \( \left(42\right) \)
Dimension $1$
CM no
Base change yes
Sign $-1$
Analytic rank odd

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Base field: \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 3\); class number \(1\).

Form

Weight: 2
Level: 1764.2 = \( \left(42\right) \)
Level norm: 1764
Dimension: 1
CM: no
Base change: yes 5082.2.a.d , 42.2.a.a
Newspace:2.0.11.1-1764.2 (dimension 3)
Sign of functional equation: $-1$
Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 4 \) 4.1 = (\( 2 \)) \( 1 \)
\( 3 \) 3.1 = (\( -a \)) \( 1 \)
\( 3 \) 3.2 = (\( a - 1 \)) \( -1 \)
\( 49 \) 49.1 = (\( 7 \)) \( -1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 5 \) 5.1 = (\( -a - 1 \)) \( -2 \)
\( 5 \) 5.2 = (\( a - 2 \)) \( -2 \)
\( 11 \) 11.1 = (\( -2 a + 1 \)) \( -4 \)
\( 23 \) 23.1 = (\( a + 4 \)) \( 8 \)
\( 23 \) 23.2 = (\( a - 5 \)) \( 8 \)
\( 31 \) 31.1 = (\( -3 a + 4 \)) \( 0 \)
\( 31 \) 31.2 = (\( 3 a + 1 \)) \( 0 \)
\( 37 \) 37.1 = (\( -3 a - 2 \)) \( -10 \)
\( 37 \) 37.2 = (\( 3 a - 5 \)) \( -10 \)
\( 47 \) 47.1 = (\( -2 a + 7 \)) \( 0 \)
\( 47 \) 47.2 = (\( 2 a + 5 \)) \( 0 \)
\( 53 \) 53.1 = (\( -4 a + 5 \)) \( 6 \)
\( 53 \) 53.2 = (\( 4 a + 1 \)) \( 6 \)
\( 59 \) 59.1 = (\( a + 7 \)) \( 4 \)
\( 59 \) 59.2 = (\( a - 8 \)) \( 4 \)
\( 67 \) 67.1 = (\( -3 a - 5 \)) \( 4 \)
\( 67 \) 67.2 = (\( 3 a - 8 \)) \( 4 \)
\( 71 \) 71.1 = (\( -5 a + 1 \)) \( 8 \)
\( 71 \) 71.2 = (\( 5 a - 4 \)) \( 8 \)
\( 89 \) 89.1 = (\( 5 a + 2 \)) \( -6 \)
Display number of eigenvalues