Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $10$ |
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:
\(x^{10} - 23x^{8} + 169x^{6} - 469x^{4} + 410x^{2} - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $-\frac{1}{48}e^{9} + \frac{5}{12}e^{7} - \frac{39}{16}e^{5} + \frac{131}{24}e^{3} - \frac{20}{3}e$ |
11 | $[11, 11, -w - 2]$ | $\phantom{-}\frac{1}{16}e^{8} - \frac{4}{3}e^{6} + \frac{137}{16}e^{4} - \frac{147}{8}e^{2} + \frac{19}{3}$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{24}e^{9} + e^{7} - \frac{63}{8}e^{5} + \frac{293}{12}e^{3} - 26e$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{12}e^{7} - \frac{7}{4}e^{5} + \frac{21}{2}e^{3} - \frac{46}{3}e$ |
16 | $[16, 2, 2]$ | $-1$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $-\frac{1}{12}e^{7} + \frac{3}{2}e^{5} - \frac{25}{4}e^{3} + \frac{17}{6}e$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{12}e^{9} - \frac{11}{6}e^{7} + \frac{25}{2}e^{5} - \frac{373}{12}e^{3} + \frac{137}{6}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $-e^{2} + 6$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{5}{48}e^{9} - \frac{29}{12}e^{7} + \frac{287}{16}e^{5} - \frac{1201}{24}e^{3} + \frac{265}{6}e$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $\phantom{-}\frac{1}{12}e^{9} - \frac{7}{4}e^{7} + \frac{43}{4}e^{5} - \frac{247}{12}e^{3} + \frac{11}{2}e$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}\frac{1}{12}e^{9} - \frac{7}{4}e^{7} + \frac{43}{4}e^{5} - \frac{247}{12}e^{3} + \frac{11}{2}e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{1}{48}e^{8} + \frac{1}{2}e^{6} - \frac{59}{16}e^{4} + \frac{179}{24}e^{2} + 3$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{1}{8}e^{9} + \frac{11}{4}e^{7} - \frac{149}{8}e^{5} + 44e^{3} - \frac{49}{2}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{5}{48}e^{8} - \frac{9}{4}e^{6} + \frac{227}{16}e^{4} - \frac{643}{24}e^{2} + 13$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{24}e^{8} - \frac{11}{12}e^{6} + \frac{53}{8}e^{4} - \frac{233}{12}e^{2} + \frac{38}{3}$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $\phantom{-}0$ |
83 | $[83, 83, -2w + 3]$ | $-\frac{1}{6}e^{8} + \frac{10}{3}e^{6} - \frac{37}{2}e^{4} + \frac{86}{3}e^{2} - \frac{4}{3}$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{17}{3}e^{7} + \frac{161}{4}e^{5} - \frac{207}{2}e^{3} + \frac{239}{3}e$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $\phantom{-}\frac{5}{24}e^{8} - \frac{13}{3}e^{6} + \frac{207}{8}e^{4} - \frac{523}{12}e^{2} + \frac{4}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$16$ | $[16, 2, 2]$ | $1$ |