Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w - 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 31x^{10} + 358x^{8} - 1867x^{6} + 4116x^{4} - 2528x^{2} + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{2}{535}e^{11} + \frac{509}{4280}e^{9} - \frac{1235}{856}e^{7} + \frac{17361}{2140}e^{5} - \frac{83167}{4280}e^{3} + \frac{5858}{535}e$ |
| 7 | $[7, 7, w - 3]$ | $\phantom{-}1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{4280}e^{10} - \frac{199}{4280}e^{8} + \frac{383}{428}e^{6} - \frac{24707}{4280}e^{4} + \frac{13663}{1070}e^{2} - \frac{2573}{535}$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}\frac{99}{17120}e^{11} - \frac{2581}{17120}e^{9} + \frac{2393}{1712}e^{7} - \frac{96273}{17120}e^{5} + \frac{45097}{4280}e^{3} - \frac{6303}{535}e$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{11}{8560}e^{10} + \frac{49}{8560}e^{8} + \frac{281}{856}e^{6} - \frac{27823}{8560}e^{4} + \frac{4023}{535}e^{2} - \frac{1096}{535}$ |
| 13 | $[13, 13, -w + 2]$ | $-\frac{11}{8560}e^{10} + \frac{49}{8560}e^{8} + \frac{281}{856}e^{6} - \frac{27823}{8560}e^{4} + \frac{4023}{535}e^{2} - \frac{1096}{535}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{99}{17120}e^{11} - \frac{2581}{17120}e^{9} + \frac{2393}{1712}e^{7} - \frac{96273}{17120}e^{5} + \frac{40817}{4280}e^{3} - \frac{2023}{535}e$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}\frac{111}{4280}e^{10} - \frac{2829}{4280}e^{8} + \frac{2495}{428}e^{6} - \frac{88877}{4280}e^{4} + \frac{13844}{535}e^{2} - \frac{2588}{535}$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}\frac{3}{160}e^{11} - \frac{97}{160}e^{9} + \frac{115}{16}e^{7} - \frac{5961}{160}e^{5} + \frac{1517}{20}e^{3} - \frac{166}{5}e$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-\frac{29}{17120}e^{11} + \frac{1491}{17120}e^{9} - \frac{2547}{1712}e^{7} + \frac{181503}{17120}e^{5} - \frac{125517}{4280}e^{3} + \frac{9693}{535}e$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $-\frac{1}{856}e^{11} + \frac{23}{214}e^{9} - \frac{1797}{856}e^{7} + \frac{13365}{856}e^{5} - \frac{38923}{856}e^{3} + \frac{3643}{107}e$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{19}{1070}e^{11} - \frac{571}{1070}e^{9} + \frac{643}{107}e^{7} - \frac{32873}{1070}e^{5} + \frac{35019}{535}e^{3} - \frac{16858}{535}e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{13}{1712}e^{11} - \frac{233}{1712}e^{9} + \frac{49}{107}e^{7} + \frac{4517}{1712}e^{5} - \frac{10381}{856}e^{3} + \frac{21}{107}e$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $\phantom{-}\frac{211}{8560}e^{10} - \frac{5609}{8560}e^{8} + \frac{5271}{856}e^{6} - \frac{205577}{8560}e^{4} + \frac{17867}{535}e^{2} - \frac{1544}{535}$ |
| 43 | $[43, 43, -2w - 3]$ | $-\frac{209}{17120}e^{11} + \frac{7351}{17120}e^{9} - \frac{9427}{1712}e^{7} + \frac{528523}{17120}e^{5} - \frac{298267}{4280}e^{3} + \frac{22758}{535}e$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $-\frac{11}{428}e^{10} + \frac{263}{428}e^{8} - \frac{528}{107}e^{6} + \frac{6417}{428}e^{4} - \frac{3233}{214}e^{2} + \frac{1180}{107}$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $-\frac{161}{8560}e^{10} + \frac{4219}{8560}e^{8} - \frac{4097}{856}e^{6} + \frac{177187}{8560}e^{4} - \frac{36559}{1070}e^{2} + \frac{3024}{535}$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $-\frac{583}{17120}e^{11} + \frac{17577}{17120}e^{9} - \frac{19561}{1712}e^{7} + \frac{969261}{17120}e^{5} - \frac{493719}{4280}e^{3} + \frac{29806}{535}e$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{11}{8560}e^{11} - \frac{49}{8560}e^{9} - \frac{281}{856}e^{7} + \frac{27823}{8560}e^{5} - \frac{3488}{535}e^{3} - \frac{3184}{535}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w - 3]$ | $-1$ |