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: | $[4, 2, 2]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $78$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - x^{17} + 28x^{16} + 11x^{15} + 502x^{14} + 275x^{13} + 4932x^{12} + 3601x^{11} + 34402x^{10} + 20105x^{9} + 137144x^{8} + 60627x^{7} + 390199x^{6} + 140346x^{5} + 587952x^{4} + 201096x^{3} + 606528x^{2} + 163296x + 46656\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 3 | $[3, 3, -2w + 19]$ | $...$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $...$ |
| 13 | $[13, 13, w + 11]$ | $...$ |
| 17 | $[17, 17, w + 3]$ | $...$ |
| 17 | $[17, 17, w + 13]$ | $...$ |
| 19 | $[19, 19, w + 6]$ | $...$ |
| 19 | $[19, 19, w + 12]$ | $...$ |
| 37 | $[37, 37, w + 2]$ | $...$ |
| 37 | $[37, 37, w + 34]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 59 | $[59, 59, -4w - 33]$ | $...$ |
| 59 | $[59, 59, 4w - 37]$ | $...$ |
| 61 | $[61, 61, w + 28]$ | $...$ |
| 61 | $[61, 61, w + 32]$ | $...$ |
| 71 | $[71, 71, w + 22]$ | $...$ |
| 71 | $[71, 71, w + 48]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{3048379096850467010457088}{474920035124315148648278552745}e^{17} - \frac{8206885324337886467176097}{1519744112397808475674491368784}e^{16} + \frac{1353335412911472002870077699}{7598720561989042378372456843920}e^{15} + \frac{365452195607318325632146381}{3799360280994521189186228421960}e^{14} + \frac{24472827520956429792607706893}{7598720561989042378372456843920}e^{13} + \frac{4133994997535446575734054477}{1899680140497260594593114210980}e^{12} + \frac{26685492748041942841028289041}{844302284665449153152495204880}e^{11} + \frac{100116887454156778701604679471}{3799360280994521189186228421960}e^{10} + \frac{1678864485156763278586973560303}{7598720561989042378372456843920}e^{9} + \frac{279632045325700182148601167847}{1899680140497260594593114210980}e^{8} + \frac{1324824033648843227477462108575}{1519744112397808475674491368784}e^{7} + \frac{529873468562419588094711839661}{1266453426998173729728742807320}e^{6} + \frac{18627690055802710625544349464133}{7598720561989042378372456843920}e^{5} + \frac{260377538963090010124709676013}{281434094888483051050831734960}e^{4} + \frac{84764483059552232800924623193}{23452841240706920920902644580}e^{3} + \frac{5160645357765029838850598185}{7035852372212076276270793374}e^{2} + \frac{2369582817576670445307012941}{651467812241858914469517905}e + \frac{636914406525850793835949743}{651467812241858914469517905}$ |
| $2$ | $[2, 2, w + 1]$ | $-\frac{3048379096850467010457088}{474920035124315148648278552745}e^{17} + \frac{8206885324337886467176097}{1519744112397808475674491368784}e^{16} - \frac{1353335412911472002870077699}{7598720561989042378372456843920}e^{15} - \frac{365452195607318325632146381}{3799360280994521189186228421960}e^{14} - \frac{24472827520956429792607706893}{7598720561989042378372456843920}e^{13} - \frac{4133994997535446575734054477}{1899680140497260594593114210980}e^{12} - \frac{26685492748041942841028289041}{844302284665449153152495204880}e^{11} - \frac{100116887454156778701604679471}{3799360280994521189186228421960}e^{10} - \frac{1678864485156763278586973560303}{7598720561989042378372456843920}e^{9} - \frac{279632045325700182148601167847}{1899680140497260594593114210980}e^{8} - \frac{1324824033648843227477462108575}{1519744112397808475674491368784}e^{7} - \frac{529873468562419588094711839661}{1266453426998173729728742807320}e^{6} - \frac{18627690055802710625544349464133}{7598720561989042378372456843920}e^{5} - \frac{260377538963090010124709676013}{281434094888483051050831734960}e^{4} - \frac{84764483059552232800924623193}{23452841240706920920902644580}e^{3} - \frac{5160645357765029838850598185}{7035852372212076276270793374}e^{2} - \frac{2369582817576670445307012941}{651467812241858914469517905}e + \frac{14553405716008120633568162}{651467812241858914469517905}$ |