Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[5,5,-w + 1]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $168$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + 2x^{7} + 9x^{6} + 4x^{5} + 36x^{4} + 23x^{3} + 64x^{2} - 21x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-\frac{2013}{17813}e^{7} - \frac{4791}{17813}e^{6} - \frac{18398}{17813}e^{5} - \frac{12336}{17813}e^{4} - \frac{64971}{17813}e^{3} - \frac{61141}{17813}e^{2} - \frac{106035}{17813}e + \frac{34470}{17813}$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, -2w + 19]$ | $\phantom{-}1$ |
5 | $[5, 5, w]$ | $\phantom{-}0$ |
5 | $[5, 5, w + 4]$ | $-\frac{2153}{53439}e^{7} - \frac{4726}{53439}e^{6} - \frac{6394}{17813}e^{5} - \frac{10964}{53439}e^{4} - \frac{24464}{17813}e^{3} - \frac{74782}{53439}e^{2} - \frac{125276}{53439}e + \frac{13643}{17813}$ |
13 | $[13, 13, w + 1]$ | $-\frac{8612}{53439}e^{7} - \frac{18904}{53439}e^{6} - \frac{25576}{17813}e^{5} - \frac{43856}{53439}e^{4} - \frac{97856}{17813}e^{3} - \frac{245689}{53439}e^{2} - \frac{501104}{53439}e + \frac{54572}{17813}$ |
13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{1511}{53439}e^{7} + \frac{1207}{53439}e^{6} + \frac{1633}{17813}e^{5} - \frac{4120}{53439}e^{4} + \frac{6248}{17813}e^{3} + \frac{19099}{53439}e^{2} - \frac{116404}{53439}e + \frac{1065}{17813}$ |
17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{131}{17813}e^{7} - \frac{697}{17813}e^{6} - \frac{2829}{17813}e^{5} - \frac{8409}{17813}e^{4} - \frac{10824}{17813}e^{3} - \frac{11029}{17813}e^{2} - \frac{59228}{17813}e - \frac{1845}{17813}$ |
17 | $[17, 17, w + 13]$ | $\phantom{-}\frac{3347}{17813}e^{7} + \frac{5444}{17813}e^{6} + \frac{29431}{17813}e^{5} + \frac{6388}{17813}e^{4} + \frac{132742}{17813}e^{3} + \frac{46326}{17813}e^{2} + \frac{251458}{17813}e - \frac{83037}{17813}$ |
19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{1118}{53439}e^{7} + \frac{3298}{53439}e^{6} + \frac{4462}{17813}e^{5} + \frac{21107}{53439}e^{4} + \frac{17072}{17813}e^{3} + \frac{52186}{53439}e^{2} + \frac{61280}{53439}e + \frac{2910}{17813}$ |
19 | $[19, 19, w + 12]$ | $-\frac{9032}{53439}e^{7} - \frac{18709}{53439}e^{6} - \frac{26360}{17813}e^{5} - \frac{39740}{53439}e^{4} - \frac{106277}{17813}e^{3} - \frac{286612}{53439}e^{2} - \frac{558827}{53439}e + \frac{61031}{17813}$ |
37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{11966}{53439}e^{7} + \frac{28798}{53439}e^{6} + \frac{38962}{17813}e^{5} + \frac{107177}{53439}e^{4} + \frac{149072}{17813}e^{3} + \frac{455686}{53439}e^{2} + \frac{684944}{53439}e + \frac{25410}{17813}$ |
37 | $[37, 37, w + 34]$ | $-\frac{12836}{53439}e^{7} - \frac{24577}{53439}e^{6} - \frac{40586}{17813}e^{5} - \frac{45212}{53439}e^{4} - \frac{157609}{17813}e^{3} - \frac{216004}{53439}e^{2} - \frac{854135}{53439}e + \frac{93575}{17813}$ |
49 | $[49, 7, -7]$ | $-\frac{1670}{17813}e^{7} - \frac{497}{17813}e^{6} - \frac{9352}{17813}e^{5} + \frac{16366}{17813}e^{4} - \frac{55918}{17813}e^{3} + \frac{49766}{17813}e^{2} - \frac{17034}{17813}e + \frac{78319}{17813}$ |
59 | $[59, 59, -4w - 33]$ | $\phantom{-}\frac{830}{17813}e^{7} + \frac{887}{17813}e^{6} + \frac{4648}{17813}e^{5} - \frac{8134}{17813}e^{4} + \frac{5392}{17813}e^{3} - \frac{24734}{17813}e^{2} + \frac{8466}{17813}e - \frac{3939}{17813}$ |
59 | $[59, 59, 4w - 37]$ | $\phantom{-}\frac{1670}{17813}e^{7} + \frac{497}{17813}e^{6} + \frac{9352}{17813}e^{5} - \frac{16366}{17813}e^{4} + \frac{55918}{17813}e^{3} - \frac{49766}{17813}e^{2} + \frac{17034}{17813}e - \frac{42693}{17813}$ |
61 | $[61, 61, w + 28]$ | $-\frac{3413}{53439}e^{7} - \frac{4141}{53439}e^{6} - \frac{8746}{17813}e^{5} + \frac{1384}{53439}e^{4} - \frac{49727}{17813}e^{3} - \frac{90673}{53439}e^{2} - \frac{298445}{53439}e + \frac{33020}{17813}$ |
61 | $[61, 61, w + 32]$ | $\phantom{-}\frac{1760}{53439}e^{7} + \frac{6817}{53439}e^{6} + \frac{9223}{17813}e^{5} + \frac{36191}{53439}e^{4} + \frac{35288}{17813}e^{3} + \frac{107869}{53439}e^{2} + \frac{409838}{53439}e + \frac{6015}{17813}$ |
71 | $[71, 71, w + 22]$ | $\phantom{-}\frac{9599}{17813}e^{7} + \frac{22899}{17813}e^{6} + \frac{92943}{17813}e^{5} + \frac{73372}{17813}e^{4} + \frac{355608}{17813}e^{3} + \frac{362343}{17813}e^{2} + \frac{710677}{17813}e + \frac{60615}{17813}$ |
71 | $[71, 71, w + 48]$ | $-\frac{1099}{17813}e^{7} - \frac{3943}{17813}e^{6} - \frac{9717}{17813}e^{5} - \frac{14168}{17813}e^{4} - \frac{22463}{17813}e^{3} - \frac{81253}{17813}e^{2} - \frac{18335}{17813}e + \frac{5280}{17813}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,-w + 1]$ | $\frac{2153}{53439}e^{7} + \frac{4726}{53439}e^{6} + \frac{6394}{17813}e^{5} + \frac{10964}{53439}e^{4} + \frac{24464}{17813}e^{3} + \frac{74782}{53439}e^{2} + \frac{125276}{53439}e - \frac{13643}{17813}$ |