Properties

Base field \(\Q(\sqrt{-3}) \)
Weight 2
Level norm 16384
Level \( \left(128\right) \)
Label 2.0.3.1-16384.1-c
Dimension 1
CM no
Base-change no
Sign -1
Analytic rank odd

Related objects

Learn more about

Base Field: \(\Q(\sqrt{-3}) \)

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

Form

Weight 2
Level 16384.1 = \( \left(128\right) \)
Label 2.0.3.1-16384.1-c
Dimension: 1
CM: no
Base change: no, but is a twist of the base-change of a form over \(\mathbb{Q}\)
Newspace:2.0.3.1-16384.1 (dimension 16)
Sign of functional equation: -1
Analytic rank: odd

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 3 \) 3.1 = (\( -2 a + 1 \)) \( 0 \)
\( 4 \) 4.1 = (\( 2 \)) \( 0 \)
\( 7 \) 7.1 = (\( -3 a + 1 \)) \( -2 \)
\( 7 \) 7.2 = (\( 3 a - 2 \)) \( 2 \)
\( 13 \) 13.1 = (\( -4 a + 1 \)) \( -2 \)
\( 13 \) 13.2 = (\( 4 a - 3 \)) \( -2 \)
\( 19 \) 19.1 = (\( -5 a + 3 \)) \( 4 \)
\( 19 \) 19.2 = (\( -5 a + 2 \)) \( -4 \)
\( 25 \) 25.1 = (\( 5 \)) \( 6 \)
\( 31 \) 31.1 = (\( -6 a + 1 \)) \( 6 \)
\( 31 \) 31.2 = (\( 6 a - 5 \)) \( -6 \)
\( 37 \) 37.1 = (\( -7 a + 4 \)) \( -2 \)
\( 37 \) 37.2 = (\( -7 a + 3 \)) \( -2 \)
\( 43 \) 43.1 = (\( -7 a + 1 \)) \( 12 \)
\( 43 \) 43.2 = (\( 7 a - 6 \)) \( -12 \)
\( 61 \) 61.1 = (\( -9 a + 5 \)) \( -10 \)
\( 61 \) 61.2 = (\( -9 a + 4 \)) \( -10 \)
\( 67 \) 67.1 = (\( 9 a - 7 \)) \( -8 \)
\( 67 \) 67.2 = (\( 9 a - 2 \)) \( 8 \)
\( 73 \) 73.1 = (\( -9 a + 1 \)) \( -2 \)
\( 73 \) 73.2 = (\( 9 a - 8 \)) \( -2 \)
\( 79 \) 79.1 = (\( 10 a - 7 \)) \( 14 \)
\( 79 \) 79.2 = (\( 10 a - 3 \)) \( -14 \)
\( 97 \) 97.1 = (\( -11 a + 3 \)) \( 2 \)
\( 97 \) 97.2 = (\( -11 a + 8 \)) \( 2 \)

Atkin-Lehner eigenvalues

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