Base field 6.6.1292517.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 6x^{2} - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19,19,-w^{5} + 5w^{3} + w^{2} - 2w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 21x^{6} - 3x^{5} + 122x^{4} - 9x^{3} - 225x^{2} + 55x + 85\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{5} + 6w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 5w + 1]$ | $-\frac{37}{87}e^{7} + \frac{1}{87}e^{6} + \frac{650}{87}e^{5} + \frac{298}{87}e^{4} - \frac{896}{29}e^{3} - \frac{444}{29}e^{2} + \frac{931}{29}e + \frac{911}{87}$ |
| 17 | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ | $-\frac{13}{87}e^{7} - \frac{2}{87}e^{6} + \frac{266}{87}e^{5} + \frac{100}{87}e^{4} - \frac{470}{29}e^{3} - \frac{127}{29}e^{2} + \frac{603}{29}e + \frac{266}{87}$ |
| 17 | $[17, 17, w^{4} - 5w^{2} - 2w + 1]$ | $-\frac{3}{29}e^{7} + \frac{4}{29}e^{6} + \frac{48}{29}e^{5} - \frac{26}{29}e^{4} - \frac{196}{29}e^{3} - \frac{50}{29}e^{2} + \frac{239}{29}e + \frac{222}{29}$ |
| 17 | $[17, 17, -w^{5} - w^{4} + 5w^{3} + 7w^{2} - 3]$ | $\phantom{-}\frac{2}{87}e^{7} + \frac{7}{87}e^{6} - \frac{61}{87}e^{5} - \frac{89}{87}e^{4} + \frac{137}{29}e^{3} + \frac{53}{29}e^{2} - \frac{211}{29}e + \frac{26}{87}$ |
| 19 | $[19, 19, 2w^{5} - 11w^{3} - 2w^{2} + 7w]$ | $\phantom{-}\frac{23}{87}e^{7} - \frac{50}{87}e^{6} - \frac{310}{87}e^{5} + \frac{499}{87}e^{4} + \frac{256}{29}e^{3} - \frac{333}{29}e^{2} + \frac{53}{29}e + \frac{125}{87}$ |
| 19 | $[19, 19, w^{5} - 5w^{3} - w^{2} + 2w - 1]$ | $-1$ |
| 37 | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ | $\phantom{-}\frac{10}{29}e^{7} + \frac{6}{29}e^{6} - \frac{189}{29}e^{5} - \frac{155}{29}e^{4} + \frac{837}{29}e^{3} + \frac{505}{29}e^{2} - \frac{903}{29}e - \frac{363}{29}$ |
| 37 | $[37, 37, -2w^{5} - w^{4} + 11w^{3} + 8w^{2} - 6w - 2]$ | $\phantom{-}\frac{11}{29}e^{7} + \frac{24}{29}e^{6} - \frac{234}{29}e^{5} - \frac{446}{29}e^{4} + \frac{1173}{29}e^{3} + \frac{1556}{29}e^{2} - \frac{1582}{29}e - \frac{988}{29}$ |
| 53 | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ | $-\frac{20}{87}e^{7} + \frac{104}{87}e^{6} + \frac{175}{87}e^{5} - \frac{1285}{87}e^{4} + \frac{22}{29}e^{3} + \frac{1065}{29}e^{2} - \frac{326}{29}e - \frac{1217}{87}$ |
| 53 | $[53, 53, w^{3} - 4w + 1]$ | $-\frac{11}{29}e^{7} - \frac{24}{29}e^{6} + \frac{234}{29}e^{5} + \frac{446}{29}e^{4} - \frac{1144}{29}e^{3} - \frac{1614}{29}e^{2} + \frac{1321}{29}e + \frac{1336}{29}$ |
| 64 | $[64, 2, -2]$ | $-\frac{5}{87}e^{7} - \frac{61}{87}e^{6} + \frac{196}{87}e^{5} + \frac{875}{87}e^{4} - \frac{415}{29}e^{3} - \frac{785}{29}e^{2} + \frac{455}{29}e + \frac{1240}{87}$ |
| 73 | $[73, 73, -3w^{5} + 17w^{3} + 3w^{2} - 12w + 1]$ | $-\frac{13}{29}e^{7} + \frac{27}{29}e^{6} + \frac{179}{29}e^{5} - \frac{248}{29}e^{4} - \frac{511}{29}e^{3} + \frac{315}{29}e^{2} + \frac{272}{29}e + \frac{266}{29}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 1]$ | $-\frac{22}{29}e^{7} + \frac{10}{29}e^{6} + \frac{352}{29}e^{5} + \frac{80}{29}e^{4} - \frac{1215}{29}e^{3} - \frac{734}{29}e^{2} + \frac{989}{29}e + \frac{816}{29}$ |
| 73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 7w^{2} + 5w + 3]$ | $-\frac{38}{87}e^{7} - \frac{133}{87}e^{6} + \frac{898}{87}e^{5} + \frac{2213}{87}e^{4} - \frac{1588}{29}e^{3} - \frac{2341}{29}e^{2} + \frac{2066}{29}e + \frac{4378}{87}$ |
| 73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 8w^{2} + 5w + 4]$ | $\phantom{-}\frac{32}{87}e^{7} - \frac{62}{87}e^{6} - \frac{454}{87}e^{5} + \frac{577}{87}e^{4} + \frac{452}{29}e^{3} - \frac{283}{29}e^{2} - \frac{244}{29}e - \frac{367}{87}$ |
| 107 | $[107, 107, -w^{4} + w^{3} + 5w^{2} - 2w - 3]$ | $-\frac{2}{87}e^{7} + \frac{167}{87}e^{6} - \frac{287}{87}e^{5} - \frac{2347}{87}e^{4} + \frac{965}{29}e^{3} + \frac{2325}{29}e^{2} - \frac{1761}{29}e - \frac{3854}{87}$ |
| 107 | $[107, 107, -3w^{5} - w^{4} + 17w^{3} + 8w^{2} - 11w - 2]$ | $\phantom{-}\frac{112}{87}e^{7} - \frac{43}{87}e^{6} - \frac{1850}{87}e^{5} - \frac{460}{87}e^{4} + \frac{2336}{29}e^{3} + \frac{1199}{29}e^{2} - \frac{2420}{29}e - \frac{3329}{87}$ |
| 109 | $[109, 109, w^{4} - 6w^{2} + 5]$ | $\phantom{-}\frac{7}{87}e^{7} - \frac{19}{87}e^{6} - \frac{83}{87}e^{5} + \frac{254}{87}e^{4} + \frac{1}{29}e^{3} - \frac{322}{29}e^{2} + \frac{320}{29}e + \frac{265}{87}$ |
| 109 | $[109, 109, -w^{5} + 6w^{3} + w^{2} - 7w + 1]$ | $-\frac{37}{87}e^{7} + \frac{1}{87}e^{6} + \frac{650}{87}e^{5} + \frac{298}{87}e^{4} - \frac{896}{29}e^{3} - \frac{415}{29}e^{2} + \frac{931}{29}e + \frac{650}{87}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w^{5} + 5w^{3} + w^{2} - 2w + 1]$ | $1$ |