Base Field: \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 1\); class number \(1\).
Form
| Weight | 2 | |
| Level | 171.1 = \( \left(-15 a + 9\right) \) | |
| Label | 2.0.3.1-171.1-a | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.3.1-171.1 | (dimension 1) |
| Sign of functional equation: | +1 | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1/3 |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = (\( -2 a + 1 \)) | \( 0 \) |
| \( 4 \) | 4.1 = (\( 2 \)) | \( -1 \) |
| \( 7 \) | 7.1 = (\( -3 a + 1 \)) | \( -4 \) |
| \( 7 \) | 7.2 = (\( 3 a - 2 \)) | \( 2 \) |
| \( 13 \) | 13.1 = (\( -4 a + 1 \)) | \( 2 \) |
| \( 13 \) | 13.2 = (\( 4 a - 3 \)) | \( -4 \) |
| \( 19 \) | 19.1 = (\( -5 a + 3 \)) | \( 1 \) |
| \( 19 \) | 19.2 = (\( -5 a + 2 \)) | \( 2 \) |
| \( 25 \) | 25.1 = (\( 5 \)) | \( -4 \) |
| \( 31 \) | 31.1 = (\( -6 a + 1 \)) | \( 8 \) |
| \( 31 \) | 31.2 = (\( 6 a - 5 \)) | \( 2 \) |
| \( 37 \) | 37.1 = (\( -7 a + 4 \)) | \( 2 \) |
| \( 37 \) | 37.2 = (\( -7 a + 3 \)) | \( 2 \) |
| \( 43 \) | 43.1 = (\( -7 a + 1 \)) | \( 8 \) |
| \( 43 \) | 43.2 = (\( 7 a - 6 \)) | \( -4 \) |
| \( 61 \) | 61.1 = (\( -9 a + 5 \)) | \( -10 \) |
| \( 61 \) | 61.2 = (\( -9 a + 4 \)) | \( 2 \) |
| \( 67 \) | 67.1 = (\( 9 a - 7 \)) | \( 2 \) |
| \( 67 \) | 67.2 = (\( 9 a - 2 \)) | \( -4 \) |
| \( 73 \) | 73.1 = (\( -9 a + 1 \)) | \( 2 \) |
| \( 73 \) | 73.2 = (\( 9 a - 8 \)) | \( 2 \) |
| \( 79 \) | 79.1 = (\( 10 a - 7 \)) | \( 8 \) |
| \( 79 \) | 79.2 = (\( 10 a - 3 \)) | \( -4 \) |
| \( 97 \) | 97.1 = (\( -11 a + 3 \)) | \( -16 \) |
| \( 97 \) | 97.2 = (\( -11 a + 8 \)) | \( 2 \) |
| \( 103 \) | 103.1 = (\( 11 a - 9 \)) | \( -16 \) |
| \( 103 \) | 103.2 = (\( 11 a - 2 \)) | \( 8 \) |
| \( 109 \) | 109.1 = (\( 12 a - 5 \)) | \( 2 \) |
| \( 109 \) | 109.2 = (\( -12 a + 7 \)) | \( -16 \) |
| \( 121 \) | 121.1 = (\( 11 \)) | \( 14 \) |
| \( 127 \) | 127.1 = (\( -13 a + 7 \)) | \( -16 \) |
| \( 127 \) | 127.2 = (\( -13 a + 6 \)) | \( 2 \) |
| \( 139 \) | 139.1 = (\( 13 a - 10 \)) | \( -16 \) |
| \( 139 \) | 139.2 = (\( 13 a - 3 \)) | \( 14 \) |
| \( 151 \) | 151.1 = (\( -14 a + 5 \)) | \( 8 \) |
| \( 151 \) | 151.2 = (\( -14 a + 9 \)) | \( 8 \) |
| \( 157 \) | 157.1 = (\( -13 a + 1 \)) | \( -10 \) |
| \( 157 \) | 157.2 = (\( 13 a - 12 \)) | \( -22 \) |
| \( 163 \) | 163.1 = (\( -14 a + 3 \)) | \( 20 \) |
| \( 163 \) | 163.2 = (\( -14 a + 11 \)) | \( 2 \) |
| \( 181 \) | 181.1 = (\( -15 a + 4 \)) | \( 20 \) |
| \( 181 \) | 181.2 = (\( -15 a + 11 \)) | \( 2 \) |
| \( 193 \) | 193.1 = (\( 16 a - 7 \)) | \( -10 \) |
| \( 193 \) | 193.2 = (\( -16 a + 9 \)) | \( -22 \) |
| \( 199 \) | 199.1 = (\( 15 a - 13 \)) | \( -16 \) |
| \( 199 \) | 199.2 = (\( 15 a - 2 \)) | \( 20 \) |
| \( 211 \) | 211.1 = (\( -15 a + 1 \)) | \( -4 \) |
| \( 211 \) | 211.2 = (\( 15 a - 14 \)) | \( 26 \) |
| \( 223 \) | 223.1 = (\( -17 a + 6 \)) | \( 8 \) |
| \( 223 \) | 223.2 = (\( -17 a + 11 \)) | \( -4 \) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = (\( -2 a + 1 \)) | \( 1 \) |
| \( 19 \) | 19.1 = (\( -5 a + 3 \)) | \( -1 \) |