Base field 4.4.18432.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14,14,\frac{1}{3}w^{3} - 3w + 2]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} + 4x^{5} - 14x^{4} - 60x^{3} - 19x^{2} + 72x + 44\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $\phantom{-}1$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $\phantom{-}\frac{1}{10}e^{5} + \frac{7}{20}e^{4} - \frac{29}{20}e^{3} - \frac{103}{20}e^{2} - \frac{19}{20}e + \frac{53}{10}$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{9}{20}e^{4} - \frac{73}{20}e^{3} - \frac{121}{20}e^{2} + \frac{147}{20}e + \frac{61}{10}$ |
| 9 | $[9, 3, w - 3]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{9}{20}e^{4} - \frac{73}{20}e^{3} - \frac{121}{20}e^{2} + \frac{147}{20}e + \frac{81}{10}$ |
| 41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $-\frac{1}{20}e^{5} - \frac{1}{20}e^{4} + \frac{17}{20}e^{3} - \frac{1}{20}e^{2} + \frac{21}{10}e + \frac{28}{5}$ |
| 41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $-\frac{3}{20}e^{5} - \frac{2}{5}e^{4} + \frac{14}{5}e^{3} + \frac{61}{10}e^{2} - \frac{149}{20}e - \frac{87}{10}$ |
| 41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $-\frac{1}{10}e^{5} - \frac{7}{20}e^{4} + \frac{39}{20}e^{3} + \frac{103}{20}e^{2} - \frac{131}{20}e - \frac{53}{10}$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $-\frac{3}{20}e^{5} - \frac{2}{5}e^{4} + \frac{14}{5}e^{3} + \frac{61}{10}e^{2} - \frac{149}{20}e - \frac{87}{10}$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{7}{10}e^{4} - \frac{17}{5}e^{3} - \frac{103}{10}e^{2} + \frac{33}{5}e + \frac{58}{5}$ |
| 47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $-\frac{9}{20}e^{5} - \frac{6}{5}e^{4} + \frac{79}{10}e^{3} + \frac{163}{10}e^{2} - \frac{257}{20}e - \frac{151}{10}$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $-\frac{3}{20}e^{5} - \frac{3}{20}e^{4} + \frac{51}{20}e^{3} - \frac{3}{20}e^{2} - \frac{27}{10}e + \frac{54}{5}$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $\phantom{-}\frac{13}{20}e^{5} + \frac{33}{20}e^{4} - \frac{231}{20}e^{3} - \frac{447}{20}e^{2} + \frac{106}{5}e + \frac{141}{5}$ |
| 89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $-\frac{2}{5}e^{5} - \frac{7}{5}e^{4} + \frac{34}{5}e^{3} + \frac{103}{5}e^{2} - \frac{46}{5}e - \frac{76}{5}$ |
| 89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $\phantom{-}\frac{7}{10}e^{5} + \frac{39}{20}e^{4} - \frac{233}{20}e^{3} - \frac{531}{20}e^{2} + \frac{217}{20}e + \frac{221}{10}$ |
| 89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $\phantom{-}\frac{3}{5}e^{5} + \frac{21}{10}e^{4} - \frac{97}{10}e^{3} - \frac{309}{10}e^{2} + \frac{83}{10}e + \frac{179}{5}$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $\phantom{-}\frac{19}{20}e^{5} + \frac{59}{20}e^{4} - \frac{313}{20}e^{3} - \frac{821}{20}e^{2} + \frac{88}{5}e + \frac{183}{5}$ |
| 97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $-\frac{11}{10}e^{5} - \frac{67}{20}e^{4} + \frac{369}{20}e^{3} + \frac{963}{20}e^{2} - \frac{461}{20}e - \frac{523}{10}$ |
| 97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $-\frac{9}{20}e^{5} - \frac{29}{20}e^{4} + \frac{143}{20}e^{3} + \frac{411}{20}e^{2} - \frac{28}{5}e - \frac{93}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,\frac{1}{3}w^{2} + w]$ | $-1$ |
| $7$ | $[7,7,\frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $-1$ |