Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, -3w + 25]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $88$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 32x^{10} + 374x^{8} + 1917x^{6} + 3808x^{4} + 931x^{2} + 49\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{89}{13748}e^{11} + \frac{535}{1964}e^{9} + \frac{56775}{13748}e^{7} + \frac{92053}{3437}e^{5} + \frac{219329}{3437}e^{3} + \frac{17277}{1964}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{75}{1964}e^{11} + \frac{17413}{13748}e^{9} + \frac{211927}{13748}e^{7} + \frac{282691}{3437}e^{5} + \frac{573117}{3437}e^{3} + \frac{48269}{1964}e$ |
| 5 | $[5, 5, -3w + 25]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w]$ | $-\frac{139}{6874}e^{11} - \frac{2199}{3437}e^{9} - \frac{7193}{982}e^{7} - \frac{248337}{6874}e^{5} - \frac{453769}{6874}e^{3} - \frac{3233}{491}e$ |
| 11 | $[11, 11, w - 9]$ | $-\frac{473}{13748}e^{10} - \frac{10999}{13748}e^{8} - \frac{68087}{13748}e^{6} + \frac{8619}{6874}e^{4} + \frac{56871}{982}e^{2} + \frac{17005}{1964}$ |
| 11 | $[11, 11, -w - 9]$ | $\phantom{-}\frac{111}{1964}e^{10} + \frac{2795}{1964}e^{8} + \frac{21621}{1964}e^{6} + \frac{10986}{491}e^{4} - \frac{13414}{491}e^{2} - \frac{1387}{1964}$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{163}{6874}e^{11} + \frac{4299}{6874}e^{9} + \frac{36819}{6874}e^{7} + \frac{52436}{3437}e^{5} + \frac{185}{491}e^{3} - \frac{17833}{982}e$ |
| 17 | $[17, 17, w + 11]$ | $-\frac{309}{3437}e^{11} - \frac{18441}{6874}e^{9} - \frac{14005}{491}e^{7} - \frac{884965}{6874}e^{5} - \frac{1471587}{6874}e^{3} - \frac{28681}{982}e$ |
| 23 | $[23, 23, w + 1]$ | $\phantom{-}\frac{341}{13748}e^{11} + \frac{12771}{13748}e^{9} + \frac{174919}{13748}e^{7} + \frac{74051}{982}e^{5} + \frac{1135895}{6874}e^{3} + \frac{33415}{1964}e$ |
| 23 | $[23, 23, w + 22]$ | $-\frac{82}{3437}e^{11} - \frac{5461}{6874}e^{9} - \frac{4805}{491}e^{7} - \frac{369333}{6874}e^{5} - \frac{804927}{6874}e^{3} - \frac{35185}{982}e$ |
| 31 | $[31, 31, 4w - 33]$ | $\phantom{-}\frac{296}{3437}e^{10} + \frac{7617}{3437}e^{8} + \frac{62075}{3437}e^{6} + \frac{155482}{3437}e^{4} - \frac{5687}{491}e^{2} - \frac{2960}{491}$ |
| 31 | $[31, 31, 4w + 33]$ | $\phantom{-}\frac{263}{3437}e^{10} + \frac{7569}{3437}e^{8} + \frac{76508}{3437}e^{6} + \frac{321261}{3437}e^{4} + \frac{68602}{491}e^{2} + \frac{9645}{491}$ |
| 37 | $[37, 37, w + 12]$ | $\phantom{-}\frac{1317}{13748}e^{11} + \frac{39187}{13748}e^{9} + \frac{415455}{13748}e^{7} + \frac{937253}{6874}e^{5} + \frac{1590923}{6874}e^{3} + \frac{112035}{1964}e$ |
| 37 | $[37, 37, w + 25]$ | $-\frac{61}{1964}e^{11} - \frac{13521}{13748}e^{9} - \frac{156053}{13748}e^{7} - \frac{392433}{6874}e^{5} - \frac{745435}{6874}e^{3} - \frac{33537}{1964}e$ |
| 53 | $[53, 53, w + 21]$ | $\phantom{-}\frac{283}{6874}e^{11} + \frac{5339}{3437}e^{9} + \frac{147883}{6874}e^{7} + \frac{892953}{6874}e^{5} + \frac{2036071}{6874}e^{3} + \frac{28536}{491}e$ |
| 53 | $[53, 53, w + 32]$ | $\phantom{-}\frac{229}{1964}e^{11} + \frac{49423}{13748}e^{9} + \frac{549617}{13748}e^{7} + \frac{658704}{3437}e^{5} + \frac{1182007}{3437}e^{3} + \frac{89535}{1964}e$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{121}{982}e^{10} + \frac{1561}{491}e^{8} + \frac{25639}{982}e^{6} + \frac{66123}{982}e^{4} - \frac{8545}{982}e^{2} - \frac{5217}{491}$ |
| 61 | $[61, 61, w - 3]$ | $\phantom{-}\frac{781}{6874}e^{10} + \frac{10879}{3437}e^{8} + \frac{208339}{6874}e^{6} + \frac{794419}{6874}e^{4} + \frac{140033}{982}e^{2} + \frac{7388}{491}$ |
| 73 | $[73, 73, w + 17]$ | $-\frac{1241}{13748}e^{11} - \frac{37291}{13748}e^{9} - \frac{399059}{13748}e^{7} - \frac{902171}{6874}e^{5} - \frac{1476359}{6874}e^{3} - \frac{38163}{1964}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -3w + 25]$ | $-1$ |