Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[12, 6, -w^{2} + w + 3]$ |
| Dimension: | $7$ |
| 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:
| \(x^{7} - 4x^{6} - 18x^{5} + 93x^{4} + 7x^{3} - 479x^{2} + 608x - 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}\frac{7}{8}e^{6} - \frac{5}{4}e^{5} - 19e^{4} + \frac{261}{8}e^{3} + \frac{725}{8}e^{2} - \frac{1507}{8}e + \frac{97}{2}$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $-\frac{1}{2}e^{6} + \frac{3}{4}e^{5} + \frac{43}{4}e^{4} - \frac{77}{4}e^{3} - \frac{101}{2}e^{2} + \frac{435}{4}e - 27$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-\frac{1}{8}e^{5} - \frac{1}{8}e^{4} + \frac{17}{8}e^{3} + \frac{1}{2}e^{2} - \frac{55}{8}e + \frac{9}{2}$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{3}{8}e^{6} - \frac{1}{2}e^{5} - \frac{33}{4}e^{4} + \frac{107}{8}e^{3} + \frac{329}{8}e^{2} - \frac{621}{8}e + \frac{21}{2}$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $-e^{6} + \frac{7}{4}e^{5} + \frac{87}{4}e^{4} - \frac{175}{4}e^{3} - 102e^{2} + \frac{977}{4}e - 71$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $-\frac{11}{8}e^{6} + 2e^{5} + \frac{119}{4}e^{4} - \frac{415}{8}e^{3} - \frac{1129}{8}e^{2} + \frac{2369}{8}e - \frac{149}{2}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{3}{8}e^{6} + \frac{3}{8}e^{5} + \frac{65}{8}e^{4} - \frac{41}{4}e^{3} - \frac{317}{8}e^{2} + \frac{247}{4}e - 7$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{5}{8}e^{5} - \frac{85}{8}e^{4} + \frac{137}{8}e^{3} + 48e^{2} - \frac{815}{8}e + \frac{73}{2}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $-e^{2} + 8$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $-e^{6} + \frac{13}{8}e^{5} + \frac{173}{8}e^{4} - \frac{333}{8}e^{3} - \frac{201}{2}e^{2} + \frac{1891}{8}e - \frac{143}{2}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{13}{8}e^{6} + \frac{17}{8}e^{5} + \frac{283}{8}e^{4} - \frac{225}{4}e^{3} - \frac{1363}{8}e^{2} + \frac{1311}{4}e - 73$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $-\frac{11}{8}e^{6} + \frac{9}{4}e^{5} + 30e^{4} - \frac{457}{8}e^{3} - \frac{1129}{8}e^{2} + \frac{2599}{8}e - \frac{203}{2}$ |
| 83 | $[83, 83, -w - 3]$ | $\phantom{-}\frac{3}{8}e^{6} - \frac{1}{2}e^{5} - \frac{33}{4}e^{4} + \frac{107}{8}e^{3} + \frac{313}{8}e^{2} - \frac{645}{8}e + \frac{57}{2}$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{1}{2}e^{6} + \frac{5}{8}e^{5} + \frac{85}{8}e^{4} - \frac{137}{8}e^{3} - 48e^{2} + \frac{807}{8}e - \frac{69}{2}$ |
| 89 | $[89, 89, 2w - 1]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{4}e^{5} - \frac{5}{2}e^{4} + \frac{55}{8}e^{3} + \frac{75}{8}e^{2} - \frac{337}{8}e + \frac{51}{2}$ |
| 101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $\phantom{-}e^{6} - \frac{9}{8}e^{5} - \frac{169}{8}e^{4} + \frac{249}{8}e^{3} + \frac{193}{2}e^{2} - \frac{1479}{8}e + \frac{123}{2}$ |
| 101 | $[101, 101, 2w^{2} - 3w - 3]$ | $\phantom{-}\frac{11}{8}e^{6} - \frac{17}{8}e^{5} - \frac{239}{8}e^{4} + 55e^{3} + \frac{1149}{8}e^{2} - 315e + 72$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |
| $4$ | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $-1$ |