Base field 4.4.12357.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 44x^{12} + 785x^{10} - 7270x^{8} + 37044x^{6} - 100776x^{4} + 129456x^{2} - 59536\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{7}{5708}e^{12} + \frac{657}{11416}e^{10} - \frac{11589}{11416}e^{8} + \frac{12187}{1427}e^{6} - \frac{101145}{2854}e^{4} + \frac{94971}{1427}e^{2} - \frac{59963}{1427}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{4}{1427}e^{12} - \frac{547}{5708}e^{10} + \frac{6925}{5708}e^{8} - \frac{20037}{2854}e^{6} + \frac{53629}{2854}e^{4} - \frac{30955}{1427}e^{2} + \frac{14744}{1427}$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{2507}{696376}e^{13} + \frac{93289}{696376}e^{11} - \frac{668597}{348188}e^{9} + \frac{4583939}{348188}e^{7} - \frac{3757384}{87047}e^{5} + \frac{10159861}{174094}e^{3} - \frac{2210010}{87047}e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{56}{1427}e^{12} - \frac{16743}{11416}e^{10} + \frac{240991}{11416}e^{8} - \frac{833593}{5708}e^{6} + \frac{702186}{1427}e^{4} - \frac{1025575}{1427}e^{2} + \frac{507513}{1427}$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $-\frac{677}{696376}e^{13} + \frac{19845}{696376}e^{11} - \frac{25980}{87047}e^{9} + \frac{475101}{348188}e^{7} - \frac{536185}{174094}e^{5} + \frac{518747}{87047}e^{3} - \frac{626938}{87047}e$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $-1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{2627}{348188}e^{13} + \frac{48339}{174094}e^{11} - \frac{1361305}{348188}e^{9} + \frac{9140223}{348188}e^{7} - \frac{29604893}{348188}e^{5} + \frac{20381633}{174094}e^{3} - \frac{4335101}{87047}e$ |
| 31 | $[31, 31, w^{3} - w^{2} - 3w + 1]$ | $-\frac{495}{11416}e^{12} + \frac{18439}{11416}e^{10} - \frac{132049}{5708}e^{8} + \frac{453673}{2854}e^{6} - \frac{1514489}{2854}e^{4} + \frac{1089279}{1427}e^{2} - \frac{518109}{1427}$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{8121}{696376}e^{13} + \frac{74203}{174094}e^{11} - \frac{4132137}{696376}e^{9} + \frac{13552109}{348188}e^{7} - \frac{10389842}{87047}e^{5} + \frac{12553438}{87047}e^{3} - \frac{4633269}{87047}e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}\frac{45}{11416}e^{12} - \frac{903}{5708}e^{10} + \frac{27771}{11416}e^{8} - \frac{101037}{5708}e^{6} + \frac{86159}{1427}e^{4} - \frac{118225}{1427}e^{2} + \frac{63187}{1427}$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w - 1]$ | $-\frac{383}{87047}e^{13} + \frac{109745}{696376}e^{11} - \frac{1520923}{696376}e^{9} + \frac{5116391}{348188}e^{7} - \frac{17068895}{348188}e^{5} + \frac{6344861}{87047}e^{3} - \frac{3271119}{87047}e$ |
| 53 | $[53, 53, -w^{2} - w + 4]$ | $-\frac{11097}{348188}e^{13} + \frac{207839}{174094}e^{11} - \frac{1500244}{87047}e^{9} + \frac{20869323}{174094}e^{7} - \frac{142241301}{348188}e^{5} + \frac{106292795}{174094}e^{3} - \frac{26711303}{87047}e$ |
| 59 | $[59, 59, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{2207}{348188}e^{13} - \frac{169633}{696376}e^{11} + \frac{2553833}{696376}e^{9} - \frac{9454633}{348188}e^{7} + \frac{35242205}{348188}e^{5} - \frac{30044779}{174094}e^{3} + \frac{9028191}{87047}e$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 8w + 1]$ | $-\frac{373}{11416}e^{12} + \frac{13733}{11416}e^{10} - \frac{97353}{5708}e^{8} + \frac{332599}{2854}e^{6} - \frac{559539}{1427}e^{4} + \frac{843279}{1427}e^{2} - \frac{446914}{1427}$ |
| 89 | $[89, 89, -2w^{3} + 3w^{2} + 8w - 8]$ | $\phantom{-}\frac{24085}{696376}e^{13} - \frac{901445}{696376}e^{11} + \frac{6494527}{348188}e^{9} - \frac{22507661}{174094}e^{7} + \frac{38144575}{87047}e^{5} - \frac{113656227}{174094}e^{3} + \frac{30128706}{87047}e$ |
| 89 | $[89, 89, w^{3} - 5w + 1]$ | $-\frac{2813}{348188}e^{13} + \frac{28747}{87047}e^{11} - \frac{1820855}{348188}e^{9} + \frac{14037275}{348188}e^{7} - \frac{54087965}{348188}e^{5} + \frac{23724554}{87047}e^{3} - \frac{14505489}{87047}e$ |
| 97 | $[97, 97, w^{3} - 6w - 1]$ | $-\frac{47}{1427}e^{12} + \frac{1696}{1427}e^{10} - \frac{93855}{5708}e^{8} + \frac{622845}{5708}e^{6} - \frac{506110}{1427}e^{4} + \frac{726536}{1427}e^{2} - \frac{345909}{1427}$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 4w - 10]$ | $\phantom{-}\frac{93}{1427}e^{12} - \frac{3447}{1427}e^{10} + \frac{98519}{2854}e^{8} - \frac{339420}{1427}e^{6} + \frac{2294649}{2854}e^{4} - \frac{1705404}{1427}e^{2} + \frac{865080}{1427}$ |
| 101 | $[101, 101, -w^{3} + 6w - 2]$ | $-\frac{7795}{348188}e^{13} + \frac{72264}{87047}e^{11} - \frac{1030804}{87047}e^{9} + \frac{14086567}{174094}e^{7} - \frac{92809205}{348188}e^{5} + \frac{64203755}{174094}e^{3} - \frac{14007720}{87047}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $1$ |