Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 84x^{10} + 2084x^{8} - 14112x^{6} + 29888x^{4} - 6144x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $-\frac{41}{75648}e^{10} + \frac{193}{4728}e^{8} - \frac{4761}{6304}e^{6} - \frac{789}{1576}e^{4} + \frac{34213}{2364}e^{2} - \frac{2411}{591}$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{319}{75648}e^{11} - \frac{26837}{75648}e^{9} + \frac{55657}{6304}e^{7} - \frac{379905}{6304}e^{5} + \frac{593525}{4728}e^{3} - \frac{25853}{2364}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{319}{75648}e^{11} - \frac{26837}{75648}e^{9} + \frac{55657}{6304}e^{7} - \frac{379905}{6304}e^{5} + \frac{593525}{4728}e^{3} - \frac{25853}{2364}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{319}{75648}e^{11} - \frac{26837}{75648}e^{9} + \frac{55657}{6304}e^{7} - \frac{379905}{6304}e^{5} + \frac{593525}{4728}e^{3} - \frac{28217}{2364}e$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{319}{75648}e^{11} - \frac{26837}{75648}e^{9} + \frac{55657}{6304}e^{7} - \frac{379905}{6304}e^{5} + \frac{593525}{4728}e^{3} - \frac{28217}{2364}e$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{6229}{453888}e^{11} + \frac{130573}{113472}e^{9} - \frac{358443}{12608}e^{7} + \frac{298943}{1576}e^{5} - \frac{5509087}{14184}e^{3} + \frac{172879}{3546}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{1}{384}e^{11} + \frac{43}{192}e^{9} - \frac{187}{32}e^{7} + \frac{735}{16}e^{5} - \frac{689}{6}e^{3} + \frac{205}{6}e$ |
| 17 | $[17, 17, w - 10]$ | $\phantom{-}\frac{395}{113472}e^{10} - \frac{1033}{3546}e^{8} + \frac{5647}{788}e^{6} - \frac{74285}{1576}e^{4} + \frac{168049}{1773}e^{2} - \frac{15652}{1773}$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{395}{113472}e^{10} - \frac{1033}{3546}e^{8} + \frac{5647}{788}e^{6} - \frac{74285}{1576}e^{4} + \frac{168049}{1773}e^{2} - \frac{15652}{1773}$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{937}{151296}e^{11} - \frac{19589}{37824}e^{9} + \frac{160353}{12608}e^{7} - \frac{32755}{394}e^{5} + \frac{781519}{4728}e^{3} - \frac{24065}{1182}e$ |
| 19 | $[19, 19, w + 15]$ | $\phantom{-}\frac{937}{151296}e^{11} - \frac{19589}{37824}e^{9} + \frac{160353}{12608}e^{7} - \frac{32755}{394}e^{5} + \frac{781519}{4728}e^{3} - \frac{24065}{1182}e$ |
| 29 | $[29, 29, -2w + 21]$ | $\phantom{-}\frac{601}{226944}e^{10} - \frac{3127}{14184}e^{8} + \frac{33805}{6304}e^{6} - \frac{6708}{197}e^{4} + \frac{483007}{7092}e^{2} - \frac{21721}{1773}$ |
| 29 | $[29, 29, 5w - 54]$ | $\phantom{-}\frac{601}{226944}e^{10} - \frac{3127}{14184}e^{8} + \frac{33805}{6304}e^{6} - \frac{6708}{197}e^{4} + \frac{483007}{7092}e^{2} - \frac{21721}{1773}$ |
| 47 | $[47, 47, w + 18]$ | $\phantom{-}\frac{529}{453888}e^{11} - \frac{22319}{226944}e^{9} + \frac{31143}{12608}e^{7} - \frac{111495}{6304}e^{5} + \frac{339329}{7092}e^{3} - \frac{284663}{7092}e$ |
| 47 | $[47, 47, w + 28]$ | $\phantom{-}\frac{529}{453888}e^{11} - \frac{22319}{226944}e^{9} + \frac{31143}{12608}e^{7} - \frac{111495}{6304}e^{5} + \frac{339329}{7092}e^{3} - \frac{284663}{7092}e$ |
| 59 | $[59, 59, w + 27]$ | $-\frac{19}{3546}e^{11} + \frac{51131}{113472}e^{9} - \frac{17653}{1576}e^{7} + \frac{239505}{3152}e^{5} - \frac{1077937}{7092}e^{3} - \frac{25933}{3546}e$ |
| 59 | $[59, 59, w + 31]$ | $-\frac{19}{3546}e^{11} + \frac{51131}{113472}e^{9} - \frac{17653}{1576}e^{7} + \frac{239505}{3152}e^{5} - \frac{1077937}{7092}e^{3} - \frac{25933}{3546}e$ |
| 71 | $[71, 71, w + 21]$ | $\phantom{-}\frac{4273}{453888}e^{11} - \frac{177929}{226944}e^{9} + \frac{240487}{12608}e^{7} - \frac{760429}{6304}e^{5} + \frac{402152}{1773}e^{3} - \frac{96617}{7092}e$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{4273}{453888}e^{11} - \frac{177929}{226944}e^{9} + \frac{240487}{12608}e^{7} - \frac{760429}{6304}e^{5} + \frac{402152}{1773}e^{3} - \frac{96617}{7092}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |