Base field \(\Q(\sqrt{109}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[20, 10, -6w + 34]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + x^{5} - 11x^{4} - 11x^{3} + 12x^{2} + 10x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 5]$ | $\phantom{-}\frac{7}{59}e^{5} - \frac{10}{59}e^{4} - \frac{78}{59}e^{3} + \frac{104}{59}e^{2} + 2e - \frac{107}{59}$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -3w + 17]$ | $-1$ |
| 5 | $[5, 5, -3w - 14]$ | $-\frac{37}{59}e^{5} - \frac{23}{59}e^{4} + \frac{387}{59}e^{3} + \frac{251}{59}e^{2} - 5e - \frac{193}{59}$ |
| 7 | $[7, 7, w - 5]$ | $-\frac{4}{59}e^{5} - \frac{28}{59}e^{4} + \frac{53}{59}e^{3} + \frac{303}{59}e^{2} - 3e - \frac{276}{59}$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{10}{59}e^{5} + \frac{11}{59}e^{4} - \frac{103}{59}e^{3} - \frac{138}{59}e^{2} + e + \frac{159}{59}$ |
| 29 | $[29, 29, -w - 7]$ | $-\frac{98}{59}e^{5} + \frac{22}{59}e^{4} + \frac{1092}{59}e^{3} - \frac{217}{59}e^{2} - 23e + \frac{141}{59}$ |
| 29 | $[29, 29, -w + 8]$ | $\phantom{-}\frac{26}{59}e^{5} + \frac{5}{59}e^{4} - \frac{315}{59}e^{3} - \frac{52}{59}e^{2} + 9e + \frac{83}{59}$ |
| 31 | $[31, 31, -5w + 28]$ | $\phantom{-}\frac{73}{59}e^{5} + \frac{39}{59}e^{4} - \frac{805}{59}e^{3} - \frac{441}{59}e^{2} + 15e + \frac{81}{59}$ |
| 31 | $[31, 31, -5w - 23]$ | $-\frac{13}{59}e^{5} + \frac{27}{59}e^{4} + \frac{187}{59}e^{3} - \frac{269}{59}e^{2} - 9e + \frac{165}{59}$ |
| 43 | $[43, 43, 6w + 29]$ | $-\frac{7}{59}e^{5} + \frac{10}{59}e^{4} + \frac{78}{59}e^{3} - \frac{104}{59}e^{2} + \frac{166}{59}$ |
| 43 | $[43, 43, -6w + 35]$ | $\phantom{-}\frac{39}{59}e^{5} + \frac{37}{59}e^{4} - \frac{384}{59}e^{3} - \frac{432}{59}e^{2} - e + \frac{272}{59}$ |
| 61 | $[61, 61, 3w - 19]$ | $\phantom{-}\frac{116}{59}e^{5} + \frac{104}{59}e^{4} - \frac{1301}{59}e^{3} - \frac{1058}{59}e^{2} + 26e + \frac{629}{59}$ |
| 61 | $[61, 61, -3w - 16]$ | $-\frac{163}{59}e^{5} - \frac{79}{59}e^{4} + \frac{1791}{59}e^{3} + \frac{857}{59}e^{2} - 31e - \frac{627}{59}$ |
| 71 | $[71, 71, -7w - 34]$ | $-\frac{7}{59}e^{5} + \frac{10}{59}e^{4} + \frac{78}{59}e^{3} - \frac{45}{59}e^{2} - 2e - \frac{424}{59}$ |
| 71 | $[71, 71, 7w - 41]$ | $-\frac{119}{59}e^{5} - \frac{66}{59}e^{4} + \frac{1267}{59}e^{3} + \frac{592}{59}e^{2} - 17e - \frac{128}{59}$ |
| 73 | $[73, 73, 2w - 7]$ | $\phantom{-}\frac{109}{59}e^{5} - \frac{63}{59}e^{4} - \frac{1223}{59}e^{3} + \frac{667}{59}e^{2} + 24e - \frac{621}{59}$ |
| 73 | $[73, 73, -2w - 5]$ | $\phantom{-}\frac{206}{59}e^{5} + \frac{85}{59}e^{4} - \frac{2228}{59}e^{3} - \frac{884}{59}e^{2} + 36e + \frac{408}{59}$ |
| 83 | $[83, 83, -w - 10]$ | $\phantom{-}\frac{139}{59}e^{5} + \frac{29}{59}e^{4} - \frac{1591}{59}e^{3} - \frac{396}{59}e^{2} + 35e + \frac{505}{59}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |
| $5$ | $[5, 5, -3w + 17]$ | $1$ |