Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 25x^{12} + 244x^{10} - 1182x^{8} + 2991x^{6} - 3773x^{4} + 2000x^{2} - 320\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{32}e^{12} - \frac{21}{32}e^{10} + \frac{39}{8}e^{8} - \frac{239}{16}e^{6} + \frac{503}{32}e^{4} + \frac{23}{32}e^{2} - \frac{7}{4}$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{5}{128}e^{13} - \frac{101}{128}e^{11} + \frac{175}{32}e^{9} - \frac{891}{64}e^{7} + \frac{347}{128}e^{5} + \frac{3479}{128}e^{3} - \frac{211}{16}e$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{1}{4}e^{12} + \frac{45}{8}e^{10} - 47e^{8} + 179e^{6} - \frac{613}{2}e^{4} + \frac{1569}{8}e^{2} - 31$ |
| 29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $-\frac{7}{16}e^{12} + \frac{155}{16}e^{10} - \frac{317}{4}e^{8} + \frac{2345}{8}e^{6} - \frac{7681}{16}e^{4} + \frac{4487}{16}e^{2} - \frac{75}{2}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{35}{128}e^{13} - \frac{787}{128}e^{11} + \frac{1641}{32}e^{9} - \frac{12477}{64}e^{7} + \frac{42909}{128}e^{5} - \frac{28655}{128}e^{3} + \frac{811}{16}e$ |
| 41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $\phantom{-}\frac{1}{4}e^{12} - \frac{45}{8}e^{10} + 47e^{8} - 180e^{6} + \frac{633}{2}e^{4} - \frac{1753}{8}e^{2} + 45$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{11}{128}e^{13} - \frac{251}{128}e^{11} + \frac{545}{32}e^{9} - \frac{4565}{64}e^{7} + \frac{19509}{128}e^{5} - \frac{20215}{128}e^{3} + \frac{899}{16}e$ |
| 47 | $[47, 47, w^{2} - 3w - 3]$ | $\phantom{-}\frac{29}{64}e^{13} - \frac{653}{64}e^{11} + \frac{1367}{16}e^{9} - \frac{10499}{32}e^{7} + \frac{36963}{64}e^{5} - \frac{25649}{64}e^{3} + \frac{629}{8}e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $-\frac{1}{8}e^{12} + \frac{23}{8}e^{10} - \frac{49}{2}e^{8} + \frac{379}{4}e^{6} - \frac{1299}{8}e^{4} + \frac{771}{8}e^{2} - 9$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}\frac{37}{128}e^{13} - \frac{821}{128}e^{11} + \frac{1679}{32}e^{9} - \frac{12347}{64}e^{7} + \frac{39451}{128}e^{5} - \frac{20601}{128}e^{3} + \frac{77}{16}e$ |
| 61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $\phantom{-}\frac{1}{4}e^{12} - \frac{23}{4}e^{10} + 49e^{8} - \frac{379}{2}e^{6} + \frac{1307}{4}e^{4} - \frac{835}{4}e^{2} + 40$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $-\frac{9}{64}e^{13} + \frac{201}{64}e^{11} - \frac{411}{16}e^{9} + \frac{2967}{32}e^{7} - \frac{8727}{64}e^{5} + \frac{2653}{64}e^{3} + \frac{191}{8}e$ |
| 67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $-\frac{1}{32}e^{13} + \frac{17}{32}e^{11} - \frac{19}{8}e^{9} - \frac{49}{16}e^{7} + \frac{1281}{32}e^{5} - \frac{2203}{32}e^{3} + \frac{95}{4}e$ |
| 67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $\phantom{-}\frac{21}{128}e^{13} - \frac{485}{128}e^{11} + \frac{1055}{32}e^{9} - \frac{8587}{64}e^{7} + \frac{32939}{128}e^{5} - \frac{25705}{128}e^{3} + \frac{605}{16}e$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $-\frac{19}{64}e^{13} + \frac{427}{64}e^{11} - \frac{889}{16}e^{9} + \frac{6749}{32}e^{7} - \frac{23293}{64}e^{5} + \frac{15975}{64}e^{3} - \frac{467}{8}e$ |
| 71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $-\frac{1}{128}e^{13} + \frac{33}{128}e^{11} - \frac{99}{32}e^{9} + \frac{1087}{64}e^{7} - \frac{5599}{128}e^{5} + \frac{6613}{128}e^{3} - \frac{441}{16}e$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $-\frac{1}{128}e^{13} + \frac{33}{128}e^{11} - \frac{99}{32}e^{9} + \frac{1087}{64}e^{7} - \frac{5599}{128}e^{5} + \frac{6613}{128}e^{3} - \frac{441}{16}e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $\phantom{-}\frac{27}{128}e^{13} - \frac{587}{128}e^{11} + \frac{1169}{32}e^{9} - \frac{8325}{64}e^{7} + \frac{26021}{128}e^{5} - \frac{15367}{128}e^{3} + \frac{563}{16}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $1$ |