Properties

Base field \(\Q(\sqrt{-3}) \)
Weight 2
Level norm 6561
Level \( \left(81\right) \)
Label 2.0.3.1-6561.1-b
Dimension 1
CM no
Base-change yes
Sign +1
Analytic rank \(0\)

Related objects

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

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

Form

Weight 2
Level 6561.1 = \( \left(81\right) \)
Label 2.0.3.1-6561.1-b
Dimension: 1
CM: no
Base change: yes, of a form over \(\mathbb{Q}\) with coefficients in \(\mathbb{Q}(\sqrt{6})\)
Newspace:2.0.3.1-6561.1 (dimension 5)
Sign of functional equation: +1
Analytic rank: \(0\)
L-ratio: 4/3

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 3 \) 3.1 = (\( -2 a + 1 \)) \( 0 \)
\( 4 \) 4.1 = (\( 2 \)) \( 2 \)
\( 7 \) 7.1 = (\( -3 a + 1 \)) \( 2 \)
\( 7 \) 7.2 = (\( 3 a - 2 \)) \( 2 \)
\( 13 \) 13.1 = (\( -4 a + 1 \)) \( -1 \)
\( 13 \) 13.2 = (\( 4 a - 3 \)) \( -1 \)
\( 19 \) 19.1 = (\( -5 a + 3 \)) \( -1 \)
\( 19 \) 19.2 = (\( -5 a + 2 \)) \( -1 \)
\( 25 \) 25.1 = (\( 5 \)) \( -4 \)
\( 31 \) 31.1 = (\( -6 a + 1 \)) \( -1 \)
\( 31 \) 31.2 = (\( 6 a - 5 \)) \( -1 \)
\( 37 \) 37.1 = (\( -7 a + 4 \)) \( 8 \)
\( 37 \) 37.2 = (\( -7 a + 3 \)) \( 8 \)
\( 43 \) 43.1 = (\( -7 a + 1 \)) \( 11 \)
\( 43 \) 43.2 = (\( 7 a - 6 \)) \( 11 \)
\( 61 \) 61.1 = (\( -9 a + 5 \)) \( 5 \)
\( 61 \) 61.2 = (\( -9 a + 4 \)) \( 5 \)
\( 67 \) 67.1 = (\( 9 a - 7 \)) \( -7 \)
\( 67 \) 67.2 = (\( 9 a - 2 \)) \( -7 \)
\( 73 \) 73.1 = (\( -9 a + 1 \)) \( 11 \)
\( 73 \) 73.2 = (\( 9 a - 8 \)) \( 11 \)
\( 79 \) 79.1 = (\( 10 a - 7 \)) \( -7 \)
\( 79 \) 79.2 = (\( 10 a - 3 \)) \( -7 \)
\( 97 \) 97.1 = (\( -11 a + 3 \)) \( -7 \)
\( 97 \) 97.2 = (\( -11 a + 8 \)) \( -7 \)
\( 103 \) 103.1 = (\( 11 a - 9 \)) \( -7 \)
\( 103 \) 103.2 = (\( 11 a - 2 \)) \( -7 \)
\( 109 \) 109.1 = (\( 12 a - 5 \)) \( -1 \)
\( 109 \) 109.2 = (\( -12 a + 7 \)) \( -1 \)
\( 121 \) 121.1 = (\( 11 \)) \( -16 \)
\( 127 \) 127.1 = (\( -13 a + 7 \)) \( -19 \)
\( 127 \) 127.2 = (\( -13 a + 6 \)) \( -19 \)
\( 139 \) 139.1 = (\( 13 a - 10 \)) \( -10 \)
\( 139 \) 139.2 = (\( 13 a - 3 \)) \( -10 \)
\( 151 \) 151.1 = (\( -14 a + 5 \)) \( 5 \)
\( 151 \) 151.2 = (\( -14 a + 9 \)) \( 5 \)
\( 157 \) 157.1 = (\( -13 a + 1 \)) \( 17 \)
\( 157 \) 157.2 = (\( 13 a - 12 \)) \( 17 \)
\( 163 \) 163.1 = (\( -14 a + 3 \)) \( -10 \)
\( 163 \) 163.2 = (\( -14 a + 11 \)) \( -10 \)
\( 181 \) 181.1 = (\( -15 a + 4 \)) \( 8 \)
\( 181 \) 181.2 = (\( -15 a + 11 \)) \( 8 \)
\( 193 \) 193.1 = (\( 16 a - 7 \)) \( 11 \)
\( 193 \) 193.2 = (\( -16 a + 9 \)) \( 11 \)
\( 199 \) 199.1 = (\( 15 a - 13 \)) \( -1 \)
\( 199 \) 199.2 = (\( 15 a - 2 \)) \( -1 \)
\( 211 \) 211.1 = (\( -15 a + 1 \)) \( -1 \)
\( 211 \) 211.2 = (\( 15 a - 14 \)) \( -1 \)
\( 223 \) 223.1 = (\( -17 a + 6 \)) \( -7 \)
\( 223 \) 223.2 = (\( -17 a + 11 \)) \( -7 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 3 \) 3.1 = (\( -2 a + 1 \)) \( -1 \)