Properties

Base field \(\Q(\sqrt{-11}) \)
Weight 2
Level norm 16384
Level \( \left(128\right) \)
Label 2.0.11.1-16384.1-a
Dimension 1
CM no
Base-change yes
Sign +1
Analytic rank \(\ge2\), even

Related objects

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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 16384.1 = \( \left(128\right) \)
Label 2.0.11.1-16384.1-a
Dimension: 1
CM: no
Base change: yes 128.2.a.a
Newspace:2.0.11.1-16384.1 (dimension 48)
Sign of functional equation: +1
Analytic rank: \(\ge2\), even

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 3 \) 3.1 = (\( -a \)) \( -2 \)
\( 3 \) 3.2 = (\( a - 1 \)) \( -2 \)
\( 4 \) 4.1 = (\( 2 \)) \( 0 \)
\( 5 \) 5.1 = (\( -a - 1 \)) \( -2 \)
\( 5 \) 5.2 = (\( a - 2 \)) \( -2 \)
\( 11 \) 11.1 = (\( -2 a + 1 \)) \( 2 \)
\( 23 \) 23.1 = (\( a + 4 \)) \( 4 \)
\( 23 \) 23.2 = (\( a - 5 \)) \( 4 \)
\( 31 \) 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 = (\( -2 a + 7 \)) \( -8 \)
\( 47 \) 47.2 = (\( 2 a + 5 \)) \( -8 \)
\( 49 \) 49.1 = (\( 7 \)) \( 2 \)
\( 53 \) 53.1 = (\( -4 a + 5 \)) \( 6 \)
\( 53 \) 53.2 = (\( 4 a + 1 \)) \( 6 \)
\( 59 \) 59.1 = (\( a + 7 \)) \( -14 \)
\( 59 \) 59.2 = (\( a - 8 \)) \( -14 \)
\( 67 \) 67.1 = (\( -3 a - 5 \)) \( -10 \)
\( 67 \) 67.2 = (\( 3 a - 8 \)) \( -10 \)
\( 71 \) 71.1 = (\( -5 a + 1 \)) \( 12 \)
\( 71 \) 71.2 = (\( 5 a - 4 \)) \( 12 \)
\( 89 \) 89.1 = (\( 5 a + 2 \)) \( -2 \)
\( 89 \) 89.2 = (\( 5 a - 7 \)) \( -2 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 4 \) 4.1 = (\( 2 \)) \( -1 \)