Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{2} + w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 4x^{5} - 34x^{4} - 104x^{3} + 349x^{2} + 668x - 1028\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, w^{3} - 5w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w + 2]$ | $-\frac{1}{64}e^{5} + \frac{1}{64}e^{4} + \frac{45}{64}e^{3} - \frac{57}{64}e^{2} - \frac{27}{4}e + \frac{109}{16}$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1}{32}e^{5} - \frac{3}{32}e^{4} - \frac{49}{32}e^{3} + \frac{103}{32}e^{2} + \frac{57}{4}e - \frac{171}{8}$ |
| 13 | $[13, 13, w^{3} - 6w + 4]$ | $-\frac{1}{32}e^{5} - \frac{1}{32}e^{4} + \frac{33}{32}e^{3} - \frac{19}{32}e^{2} - \frac{27}{4}e + \frac{103}{8}$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{16}e^{4} - \frac{1}{8}e^{3} + \frac{23}{16}e^{2} + \frac{3}{4}e - \frac{27}{4}$ |
| 17 | $[17, 17, w^{2} + w - 2]$ | $-1$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}\frac{1}{64}e^{5} + \frac{11}{64}e^{4} + \frac{11}{64}e^{3} - \frac{219}{64}e^{2} - 6e + \frac{247}{16}$ |
| 23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $\phantom{-}\frac{1}{16}e^{5} - \frac{1}{16}e^{4} - \frac{41}{16}e^{3} + \frac{61}{16}e^{2} + 22e - \frac{129}{4}$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $-\frac{3}{64}e^{5} + \frac{3}{64}e^{4} + \frac{119}{64}e^{3} - \frac{187}{64}e^{2} - \frac{61}{4}e + \frac{375}{16}$ |
| 25 | $[25, 5, -w^{2} + 3]$ | $-\frac{3}{64}e^{5} + \frac{7}{64}e^{4} + \frac{143}{64}e^{3} - \frac{231}{64}e^{2} - \frac{39}{2}e + \frac{371}{16}$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $-\frac{1}{64}e^{5} + \frac{5}{64}e^{4} + \frac{53}{64}e^{3} - \frac{149}{64}e^{2} - \frac{15}{2}e + \frac{265}{16}$ |
| 29 | $[29, 29, -w^{2} - 2w + 3]$ | $\phantom{-}\frac{1}{16}e^{5} - \frac{39}{16}e^{3} + \frac{11}{8}e^{2} + \frac{81}{4}e - \frac{25}{2}$ |
| 29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $-\frac{1}{16}e^{5} - \frac{1}{16}e^{4} + \frac{33}{16}e^{3} - \frac{11}{16}e^{2} - 15e + \frac{67}{4}$ |
| 43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $\phantom{-}\frac{1}{64}e^{5} - \frac{1}{64}e^{4} - \frac{29}{64}e^{3} + \frac{105}{64}e^{2} + \frac{13}{4}e - \frac{237}{16}$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $-\frac{5}{64}e^{5} - \frac{7}{64}e^{4} + \frac{169}{64}e^{3} + \frac{55}{64}e^{2} - 20e + \frac{125}{16}$ |
| 53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $\phantom{-}\frac{7}{64}e^{5} + \frac{13}{64}e^{4} - \frac{211}{64}e^{3} - \frac{29}{64}e^{2} + 23e - \frac{319}{16}$ |
| 53 | $[53, 53, w^{2} + 2w - 5]$ | $-\frac{1}{64}e^{5} + \frac{1}{64}e^{4} + \frac{45}{64}e^{3} - \frac{89}{64}e^{2} - \frac{33}{4}e + \frac{221}{16}$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $\phantom{-}\frac{5}{32}e^{5} + \frac{13}{32}e^{4} - \frac{141}{32}e^{3} - \frac{145}{32}e^{2} + \frac{111}{4}e - \frac{67}{8}$ |
| 61 | $[61, 61, w^{3} - 7w + 3]$ | $\phantom{-}\frac{5}{32}e^{5} + \frac{7}{32}e^{4} - \frac{161}{32}e^{3} + \frac{1}{32}e^{2} + \frac{71}{2}e - \frac{285}{8}$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $\phantom{-}\frac{7}{64}e^{5} - \frac{15}{64}e^{4} - \frac{331}{64}e^{3} + \frac{487}{64}e^{2} + \frac{189}{4}e - \frac{803}{16}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{2} + w - 2]$ | $1$ |