Base field 4.4.16609.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + x^{6} - 18x^{5} - 17x^{4} + 78x^{3} + 72x^{2} - 20x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + w + 4]$ | $-1$ |
| 3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 4]$ | $\phantom{-}\frac{1}{60}e^{6} - \frac{7}{60}e^{5} - \frac{11}{30}e^{4} + \frac{33}{20}e^{3} + \frac{21}{10}e^{2} - \frac{23}{5}e - \frac{23}{15}$ |
| 8 | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $-\frac{17}{60}e^{6} - \frac{1}{60}e^{5} + \frac{157}{30}e^{4} - \frac{1}{20}e^{3} - \frac{237}{10}e^{2} + \frac{1}{5}e + \frac{151}{15}$ |
| 27 | $[27, 3, -w^{3} + 4w - 2]$ | $-\frac{4}{15}e^{6} - \frac{2}{15}e^{5} + \frac{73}{15}e^{4} + \frac{13}{5}e^{3} - \frac{108}{5}e^{2} - \frac{62}{5}e + \frac{68}{15}$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - \frac{9}{2}e^{4} - \frac{17}{4}e^{3} + \frac{39}{2}e^{2} + 18e - 3$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - \frac{9}{2}e^{4} - \frac{17}{4}e^{3} + \frac{39}{2}e^{2} + 16e - 7$ |
| 37 | $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ | $\phantom{-}\frac{17}{60}e^{6} + \frac{1}{60}e^{5} - \frac{157}{30}e^{4} - \frac{19}{20}e^{3} + \frac{237}{10}e^{2} + \frac{44}{5}e - \frac{151}{15}$ |
| 41 | $[41, 41, w^{3} - w^{2} - 5w + 2]$ | $\phantom{-}\frac{3}{20}e^{6} - \frac{1}{20}e^{5} - \frac{23}{10}e^{4} + \frac{17}{20}e^{3} + \frac{69}{10}e^{2} - \frac{17}{5}e + \frac{11}{5}$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{4}{15}e^{6} - \frac{2}{15}e^{5} + \frac{73}{15}e^{4} + \frac{8}{5}e^{3} - \frac{108}{5}e^{2} - \frac{12}{5}e + \frac{128}{15}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $-\frac{1}{4}e^{6} - \frac{1}{4}e^{5} + \frac{9}{2}e^{4} + \frac{17}{4}e^{3} - \frac{39}{2}e^{2} - 16e + 3$ |
| 61 | $[61, 61, 2w^{2} - w - 8]$ | $\phantom{-}\frac{23}{60}e^{6} + \frac{19}{60}e^{5} - \frac{193}{30}e^{4} - \frac{101}{20}e^{3} + \frac{253}{10}e^{2} + \frac{96}{5}e - \frac{109}{15}$ |
| 67 | $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ | $\phantom{-}\frac{4}{15}e^{6} + \frac{2}{15}e^{5} - \frac{73}{15}e^{4} - \frac{13}{5}e^{3} + \frac{103}{5}e^{2} + \frac{77}{5}e - \frac{8}{15}$ |
| 73 | $[73, 73, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - \frac{9}{2}e^{4} - \frac{17}{4}e^{3} + \frac{37}{2}e^{2} + 16e + 5$ |
| 79 | $[79, 79, w^{2} - 2w - 4]$ | $\phantom{-}\frac{2}{3}e^{6} + \frac{1}{3}e^{5} - \frac{38}{3}e^{4} - 5e^{3} + 59e^{2} + 19e - \frac{52}{3}$ |
| 89 | $[89, 89, w^{2} + w - 5]$ | $-\frac{1}{60}e^{6} + \frac{7}{60}e^{5} + \frac{11}{30}e^{4} - \frac{33}{20}e^{3} - \frac{31}{10}e^{2} + \frac{33}{5}e + \frac{143}{15}$ |
| 89 | $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ | $-\frac{11}{20}e^{6} - \frac{3}{20}e^{5} + \frac{101}{10}e^{4} + \frac{51}{20}e^{3} - \frac{453}{10}e^{2} - \frac{56}{5}e + \frac{93}{5}$ |
| 89 | $[89, 89, w^{3} - 5w - 5]$ | $-\frac{11}{12}e^{6} - \frac{7}{12}e^{5} + \frac{97}{6}e^{4} + \frac{33}{4}e^{3} - \frac{135}{2}e^{2} - 28e + \frac{49}{3}$ |
| 89 | $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{13}{20}e^{6} - \frac{9}{20}e^{5} + \frac{113}{10}e^{4} + \frac{133}{20}e^{3} - \frac{449}{10}e^{2} - \frac{118}{5}e + \frac{19}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + w + 4]$ | $1$ |
| $8$ | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $1$ |