Base field 4.4.7600.1
Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[36, 6, w^{3} - 2w^{2} - 4w + 9]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 2x^{5} - 36x^{4} - 60x^{3} + 232x^{2} + 224x - 320\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{2} - w + 4]$ | $\phantom{-}1$ |
| 9 | $[9, 3, w^{2} - w - 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{1}{136}e^{5} - \frac{1}{136}e^{4} + \frac{5}{34}e^{3} + \frac{5}{17}e^{2} + \frac{3}{2}e + \frac{6}{17}$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{1}{68}e^{5} + \frac{1}{68}e^{4} - \frac{37}{68}e^{3} - \frac{10}{17}e^{2} + 3e + \frac{56}{17}$ |
| 19 | $[19, 19, -w]$ | $-\frac{1}{272}e^{5} - \frac{9}{136}e^{4} + \frac{5}{68}e^{3} + \frac{163}{68}e^{2} + \frac{1}{2}e - \frac{150}{17}$ |
| 19 | $[19, 19, -w^{2} - w + 6]$ | $-\frac{1}{68}e^{5} - \frac{1}{68}e^{4} + \frac{37}{68}e^{3} + \frac{3}{34}e^{2} - 3e + \frac{80}{17}$ |
| 19 | $[19, 19, -w^{2} + w + 6]$ | $\phantom{-}\frac{11}{272}e^{5} + \frac{7}{68}e^{4} - \frac{89}{68}e^{3} - \frac{195}{68}e^{2} + 5e + \frac{120}{17}$ |
| 25 | $[25, 5, 2w^{2} - 9]$ | $-\frac{5}{272}e^{5} - \frac{11}{136}e^{4} + \frac{21}{34}e^{3} + \frac{169}{68}e^{2} - \frac{7}{2}e - \frac{138}{17}$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{5}{272}e^{5} - \frac{3}{68}e^{4} - \frac{21}{34}e^{3} + \frac{103}{68}e^{2} + 3e - \frac{100}{17}$ |
| 29 | $[29, 29, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{7}{272}e^{5} + \frac{3}{34}e^{4} - \frac{13}{17}e^{3} - \frac{189}{68}e^{2} + e + \frac{200}{17}$ |
| 41 | $[41, 41, 2w^{2} - w - 7]$ | $\phantom{-}\frac{9}{272}e^{5} - \frac{1}{34}e^{4} - \frac{79}{68}e^{3} + \frac{63}{68}e^{2} + 6e - \frac{44}{17}$ |
| 41 | $[41, 41, w^{3} - w^{2} - 6w + 4]$ | $-\frac{5}{272}e^{5} + \frac{3}{68}e^{4} + \frac{21}{34}e^{3} - \frac{103}{68}e^{2} - 3e + \frac{66}{17}$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ | $-\frac{11}{272}e^{5} - \frac{7}{68}e^{4} + \frac{89}{68}e^{3} + \frac{195}{68}e^{2} - 4e - \frac{154}{17}$ |
| 61 | $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ | $-\frac{15}{272}e^{5} - \frac{2}{17}e^{4} + \frac{63}{34}e^{3} + \frac{201}{68}e^{2} - 9e - \frac{74}{17}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ | $\phantom{-}\frac{1}{34}e^{5} - \frac{13}{136}e^{4} - \frac{37}{34}e^{3} + \frac{113}{34}e^{2} + \frac{13}{2}e - \frac{194}{17}$ |
| 61 | $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ | $\phantom{-}\frac{3}{136}e^{5} + \frac{5}{34}e^{4} - \frac{47}{68}e^{3} - \frac{149}{34}e^{2} + 2e + \frac{186}{17}$ |
| 89 | $[89, 89, -w^{3} + w^{2} + 6w - 9]$ | $\phantom{-}\frac{3}{68}e^{5} + \frac{3}{68}e^{4} - \frac{47}{34}e^{3} - \frac{13}{17}e^{2} + 3e - \frac{70}{17}$ |
| 89 | $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ | $-\frac{7}{272}e^{5} + \frac{5}{136}e^{4} + \frac{69}{68}e^{3} - \frac{83}{68}e^{2} - \frac{17}{2}e + \frac{140}{17}$ |
| 109 | $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ | $-\frac{1}{34}e^{5} - \frac{1}{34}e^{4} + \frac{37}{34}e^{3} + \frac{20}{17}e^{2} - 7e - \frac{180}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{3} + w^{2} + 5w - 6]$ | $-1$ |
| $9$ | $[9, 3, -w^{2} - w + 4]$ | $-1$ |