Base field 3.3.1489.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $12$ |
| 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:
| \(x^{12} - 62x^{10} + 1400x^{8} - 13972x^{6} + 60224x^{4} - 96000x^{2} + 16384\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $-\frac{249}{151168}e^{10} + \frac{7169}{75584}e^{8} - \frac{17805}{9448}e^{6} + \frac{554789}{37792}e^{4} - \frac{334117}{9448}e^{2} + \frac{8838}{1181}$ |
| 17 | $[17, 17, w - 1]$ | $-\frac{385}{1209344}e^{11} + \frac{11151}{604672}e^{9} - \frac{54647}{151168}e^{7} + \frac{795237}{302336}e^{5} - \frac{82731}{18896}e^{3} - \frac{25837}{4724}e$ |
| 19 | $[19, 19, -w^{2} + 2w + 6]$ | $\phantom{-}\frac{871}{604672}e^{11} - \frac{25485}{302336}e^{9} + \frac{130127}{75584}e^{7} - \frac{2133971}{151168}e^{5} + \frac{729407}{18896}e^{3} - \frac{43887}{2362}e$ |
| 19 | $[19, 19, -w^{2} + 2w + 10]$ | $-\frac{449}{302336}e^{10} + \frac{12747}{151168}e^{8} - \frac{62633}{37792}e^{6} + \frac{965077}{75584}e^{4} - \frac{273849}{9448}e^{2} - \frac{1380}{1181}$ |
| 19 | $[19, 19, -w + 3]$ | $\phantom{-}\frac{33}{1209344}e^{11} - \frac{11}{604672}e^{9} - \frac{6991}{151168}e^{7} + \frac{337291}{302336}e^{5} - \frac{343863}{37792}e^{3} + \frac{47993}{2362}e$ |
| 23 | $[23, 23, w - 2]$ | $-\frac{281}{604672}e^{11} + \frac{7967}{302336}e^{9} - \frac{39603}{75584}e^{7} + \frac{639709}{151168}e^{5} - \frac{28247}{2362}e^{3} + \frac{10981}{1181}e$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{281}{302336}e^{10} - \frac{7967}{151168}e^{8} + \frac{39603}{37792}e^{6} - \frac{639709}{75584}e^{4} + \frac{27066}{1181}e^{2} - \frac{5428}{1181}$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $-\frac{287}{1209344}e^{11} + \frac{7969}{604672}e^{9} - \frac{37473}{151168}e^{7} + \frac{506235}{302336}e^{5} - \frac{22463}{18896}e^{3} - \frac{53359}{4724}e$ |
| 31 | $[31, 31, w^{2} - 3w - 6]$ | $-\frac{481}{151168}e^{10} + \frac{13545}{75584}e^{8} - \frac{33313}{9448}e^{6} + \frac{1049997}{37792}e^{4} - \frac{665533}{9448}e^{2} + \frac{25240}{1181}$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{131}{1209344}e^{11} - \frac{3193}{604672}e^{9} + \frac{10183}{151168}e^{7} + \frac{48289}{302336}e^{5} - \frac{223327}{37792}e^{3} + \frac{17116}{1181}e$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $-\frac{281}{604672}e^{11} + \frac{7967}{302336}e^{9} - \frac{39603}{75584}e^{7} + \frac{639709}{151168}e^{5} - \frac{28247}{2362}e^{3} + \frac{12162}{1181}e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{947}{1209344}e^{11} + \frac{27085}{604672}e^{9} - \frac{133853}{151168}e^{7} + \frac{2074655}{302336}e^{5} - \frac{308707}{18896}e^{3} + \frac{18087}{4724}e$ |
| 43 | $[43, 43, w^{2} - 3w - 10]$ | $\phantom{-}\frac{253}{302336}e^{10} - \frac{6383}{151168}e^{8} + \frac{28285}{37792}e^{6} - \frac{424865}{75584}e^{4} + \frac{155601}{9448}e^{2} - \frac{4988}{1181}$ |
| 47 | $[47, 47, -w - 4]$ | $\phantom{-}\frac{379}{151168}e^{10} - \frac{11149}{75584}e^{8} + \frac{56777}{18896}e^{6} - \frac{909815}{37792}e^{4} + \frac{70094}{1181}e^{2} - \frac{13936}{1181}$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}\frac{1461}{604672}e^{11} - \frac{43003}{302336}e^{9} + \frac{220651}{75584}e^{7} - \frac{3628233}{151168}e^{5} + \frac{616419}{9448}e^{3} - \frac{35268}{1181}e$ |
| 47 | $[47, 47, -2w^{2} + 3w + 17]$ | $-\frac{541}{1209344}e^{11} + \frac{15927}{604672}e^{9} - \frac{81937}{151168}e^{7} + \frac{1349761}{302336}e^{5} - \frac{452611}{37792}e^{3} + \frac{5584}{1181}e$ |
| 49 | $[49, 7, w^{2} - w - 10]$ | $-\frac{91}{302336}e^{11} + \frac{1393}{75584}e^{9} - \frac{28689}{75584}e^{7} + \frac{216395}{75584}e^{5} - \frac{166121}{37792}e^{3} - \frac{42701}{4724}e$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{133}{604672}e^{11} + \frac{3981}{302336}e^{9} - \frac{10051}{37792}e^{7} + \frac{288289}{151168}e^{5} - \frac{45585}{37792}e^{3} - \frac{74947}{4724}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $-1$ |