Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[14, 14, w - 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 20x^{3} - 17x^{2} + 108x - 54\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $-\frac{2}{33}e^{4} + \frac{8}{33}e^{3} + \frac{25}{33}e^{2} - \frac{116}{33}e + \frac{28}{11}$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $-\frac{2}{11}e^{4} - \frac{3}{11}e^{3} + \frac{25}{11}e^{2} + \frac{16}{11}e - \frac{26}{11}$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{33}e^{4} - \frac{4}{33}e^{3} - \frac{29}{33}e^{2} + \frac{25}{33}e + \frac{30}{11}$ |
| 19 | $[19, 19, -w + 2]$ | $-\frac{4}{33}e^{4} - \frac{17}{33}e^{3} + \frac{50}{33}e^{2} + \frac{131}{33}e - \frac{32}{11}$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $-\frac{4}{33}e^{4} - \frac{17}{33}e^{3} + \frac{83}{33}e^{2} + \frac{230}{33}e - \frac{120}{11}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $\phantom{-}\frac{1}{11}e^{4} + \frac{7}{11}e^{3} - \frac{7}{11}e^{2} - \frac{74}{11}e + \frac{46}{11}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{7}{33}e^{4} + \frac{5}{33}e^{3} - \frac{104}{33}e^{2} + \frac{10}{33}e + \frac{56}{11}$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $\phantom{-}\frac{4}{33}e^{4} - \frac{16}{33}e^{3} - \frac{50}{33}e^{2} + \frac{265}{33}e - \frac{12}{11}$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $-\frac{1}{33}e^{4} + \frac{4}{33}e^{3} + \frac{62}{33}e^{2} - \frac{25}{33}e - \frac{96}{11}$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $-\frac{1}{11}e^{4} - \frac{7}{11}e^{3} + \frac{7}{11}e^{2} + \frac{74}{11}e - \frac{24}{11}$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $\phantom{-}\frac{5}{33}e^{4} + \frac{13}{33}e^{3} - \frac{79}{33}e^{2} - \frac{106}{33}e + \frac{106}{11}$ |
| 47 | $[47, 47, -2w + 7]$ | $\phantom{-}\frac{1}{33}e^{4} + \frac{29}{33}e^{3} - \frac{29}{33}e^{2} - \frac{338}{33}e + \frac{162}{11}$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{11}e^{4} - \frac{4}{11}e^{3} - \frac{18}{11}e^{2} + \frac{47}{11}e + \frac{24}{11}$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}\frac{8}{33}e^{4} + \frac{1}{33}e^{3} - \frac{133}{33}e^{2} + \frac{2}{33}e + \frac{64}{11}$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $\phantom{-}\frac{1}{11}e^{4} - \frac{4}{11}e^{3} - \frac{18}{11}e^{2} + \frac{47}{11}e - \frac{20}{11}$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $\phantom{-}\frac{4}{11}e^{4} + \frac{6}{11}e^{3} - \frac{50}{11}e^{2} - \frac{32}{11}e + \frac{118}{11}$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{8}{33}e^{4} + \frac{34}{33}e^{3} - \frac{100}{33}e^{2} - \frac{328}{33}e + \frac{196}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 1]$ | $1$ |
| $7$ | $[7, 7, -2w^{2} + 3w + 16]$ | $-1$ |