Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 18x^{6} + 14x^{5} + 95x^{4} - 51x^{3} - 136x^{2} + 36x + 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{5}{128}e^{7} - \frac{7}{128}e^{6} - \frac{25}{32}e^{5} + \frac{55}{64}e^{4} + \frac{559}{128}e^{3} - \frac{453}{128}e^{2} - \frac{307}{64}e + \frac{25}{8}$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{17}{128}e^{7} - \frac{11}{128}e^{6} - \frac{69}{32}e^{5} + \frac{59}{64}e^{4} + \frac{1235}{128}e^{3} - \frac{273}{128}e^{2} - \frac{615}{64}e + \frac{5}{8}$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $\phantom{-}\frac{7}{128}e^{7} + \frac{3}{128}e^{6} - \frac{35}{32}e^{5} - \frac{51}{64}e^{4} + \frac{885}{128}e^{3} + \frac{761}{128}e^{2} - \frac{801}{64}e - \frac{45}{8}$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $-\frac{13}{128}e^{7} + \frac{31}{128}e^{6} + \frac{49}{32}e^{5} - \frac{207}{64}e^{4} - \frac{839}{128}e^{3} + \frac{1421}{128}e^{2} + \frac{523}{64}e - \frac{65}{8}$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-2e + 2$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{64}e^{7} + \frac{5}{64}e^{6} - \frac{5}{16}e^{5} - \frac{53}{32}e^{4} + \frac{99}{64}e^{3} + \frac{607}{64}e^{2} + \frac{9}{32}e - \frac{27}{4}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{32}e^{7} + \frac{5}{32}e^{6} - \frac{5}{8}e^{5} - \frac{37}{16}e^{4} + \frac{99}{32}e^{3} + \frac{255}{32}e^{2} - \frac{23}{16}e - \frac{5}{2}$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $-\frac{3}{32}e^{7} + \frac{1}{32}e^{6} + \frac{15}{8}e^{5} - \frac{1}{16}e^{4} - \frac{361}{32}e^{3} - \frac{77}{32}e^{2} + \frac{293}{16}e + \frac{5}{2}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $-\frac{31}{128}e^{7} + \frac{5}{128}e^{6} + \frac{139}{32}e^{5} - \frac{21}{64}e^{4} - \frac{2749}{128}e^{3} + \frac{31}{128}e^{2} + \frac{1449}{64}e + \frac{21}{8}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-\frac{15}{128}e^{7} + \frac{21}{128}e^{6} + \frac{59}{32}e^{5} - \frac{101}{64}e^{4} - \frac{1037}{128}e^{3} - \frac{49}{128}e^{2} + \frac{505}{64}e + \frac{85}{8}$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $\phantom{-}\frac{7}{128}e^{7} + \frac{3}{128}e^{6} - \frac{35}{32}e^{5} - \frac{51}{64}e^{4} + \frac{885}{128}e^{3} + \frac{505}{128}e^{2} - \frac{929}{64}e + \frac{19}{8}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{9}{128}e^{7} + \frac{13}{128}e^{6} - \frac{45}{32}e^{5} - \frac{93}{64}e^{4} + \frac{1083}{128}e^{3} + \frac{695}{128}e^{2} - \frac{1039}{64}e - \frac{35}{8}$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $-\frac{27}{128}e^{7} + \frac{25}{128}e^{6} + \frac{119}{32}e^{5} - \frac{105}{64}e^{4} - \frac{2353}{128}e^{3} - \frac{101}{128}e^{2} + \frac{1229}{64}e + \frac{41}{8}$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $-\frac{21}{64}e^{7} + \frac{23}{64}e^{6} + \frac{89}{16}e^{5} - \frac{167}{32}e^{4} - \frac{1631}{64}e^{3} + \frac{1205}{64}e^{2} + \frac{739}{32}e - \frac{25}{4}$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{9}{128}e^{7} + \frac{51}{128}e^{6} + \frac{29}{32}e^{5} - \frac{419}{64}e^{4} - \frac{187}{128}e^{3} + \frac{3593}{128}e^{2} - \frac{465}{64}e - \frac{157}{8}$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}\frac{3}{128}e^{7} - \frac{17}{128}e^{6} - \frac{15}{32}e^{5} + \frac{161}{64}e^{4} + \frac{489}{128}e^{3} - \frac{1667}{128}e^{2} - \frac{581}{64}e + \frac{79}{8}$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $\phantom{-}\frac{27}{128}e^{7} - \frac{25}{128}e^{6} - \frac{103}{32}e^{5} + \frac{169}{64}e^{4} + \frac{1585}{128}e^{3} - \frac{1051}{128}e^{2} - \frac{429}{64}e + \frac{23}{8}$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $-\frac{5}{64}e^{7} - \frac{25}{64}e^{6} + \frac{25}{16}e^{5} + \frac{201}{32}e^{4} - \frac{623}{64}e^{3} - \frac{1627}{64}e^{2} + \frac{563}{32}e + \frac{63}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $-1$ |