Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + 3w + 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 20x^{10} + 147x^{8} - 484x^{6} + 700x^{4} - 400x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 2w - 3]$ | $\phantom{-}\frac{5}{32}e^{11} - 3e^{9} + \frac{655}{32}e^{7} - \frac{233}{4}e^{5} + \frac{487}{8}e^{3} - 16e$ |
| 5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 2$ |
| 8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{1}{32}e^{11} + \frac{5}{8}e^{9} - \frac{139}{32}e^{7} + \frac{93}{8}e^{5} - \frac{57}{8}e^{3} - 4e$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{1}{8}e^{11} + \frac{19}{8}e^{9} - \frac{129}{8}e^{7} + \frac{373}{8}e^{5} - \frac{215}{4}e^{3} + 23e$ |
| 17 | $[17, 17, -w^{2} + 3w + 1]$ | $-1$ |
| 23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}\frac{1}{16}e^{11} - e^{9} + \frac{83}{16}e^{7} - \frac{17}{2}e^{5} - \frac{13}{4}e^{3} + 12e$ |
| 25 | $[25, 5, -w^{2} + 2w + 1]$ | $-\frac{3}{32}e^{11} + \frac{13}{8}e^{9} - \frac{305}{32}e^{7} + \frac{165}{8}e^{5} - \frac{67}{8}e^{3} - 8e$ |
| 37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $-\frac{1}{16}e^{11} + \frac{5}{4}e^{9} - \frac{155}{16}e^{7} + \frac{147}{4}e^{5} - \frac{267}{4}e^{3} + 37e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{8}e^{11} - \frac{19}{8}e^{9} + \frac{133}{8}e^{7} - \frac{421}{8}e^{5} + \frac{297}{4}e^{3} - 40e$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $\phantom{-}\frac{1}{32}e^{11} - \frac{5}{8}e^{9} + \frac{155}{32}e^{7} - \frac{145}{8}e^{5} + \frac{241}{8}e^{3} - 11e$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $-\frac{1}{8}e^{9} + \frac{7}{4}e^{7} - \frac{55}{8}e^{5} + \frac{21}{4}e^{3} + 3e$ |
| 59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $-\frac{1}{8}e^{10} + 2e^{8} - \frac{87}{8}e^{6} + \frac{45}{2}e^{4} - \frac{21}{2}e^{2} - 3$ |
| 67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $\phantom{-}\frac{1}{8}e^{10} - \frac{5}{2}e^{8} + \frac{147}{8}e^{6} - \frac{117}{2}e^{4} + \frac{137}{2}e^{2} - 13$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}\frac{9}{32}e^{11} - \frac{45}{8}e^{9} + \frac{1299}{32}e^{7} - \frac{1001}{8}e^{5} + \frac{1185}{8}e^{3} - 49e$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{4}e^{8} - 4e^{6} + \frac{81}{4}e^{4} - \frac{63}{2}e^{2} + 8$ |
| 79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $\phantom{-}\frac{3}{16}e^{11} - \frac{15}{4}e^{9} + \frac{433}{16}e^{7} - \frac{333}{4}e^{5} + \frac{389}{4}e^{3} - 29e$ |
| 79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $\phantom{-}\frac{5}{16}e^{11} - \frac{49}{8}e^{9} + \frac{699}{16}e^{7} - \frac{1091}{8}e^{5} + 175e^{3} - 71e$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{4}e^{10} + 5e^{8} - \frac{143}{4}e^{6} + 107e^{4} - 117e^{2} + 39$ |
| 83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $\phantom{-}\frac{15}{32}e^{11} - 9e^{9} + \frac{1997}{32}e^{7} - \frac{747}{4}e^{5} + \frac{1765}{8}e^{3} - 69e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + 3w + 1]$ | $1$ |