Base field \(\Q(\sqrt{493}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 123\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w]$ |
| Dimension: | $32$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $66$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{32} + 61x^{30} + 1642x^{28} + 25761x^{26} + 262296x^{24} + 1828548x^{22} + 8984740x^{20} + 31592088x^{18} + 79937124x^{16} + 145179905x^{14} + 187225755x^{12} + 167976521x^{10} + 101418818x^{8} + 39097844x^{6} + 8823489x^{4} + 992188x^{2} + 38416\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 13 | $[13, 13, w - 11]$ | $...$ |
| 13 | $[13, 13, w + 10]$ | $...$ |
| 17 | $[17, 17, w + 8]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, w + 14]$ | $...$ |
| 31 | $[31, 31, w + 5]$ | $...$ |
| 31 | $[31, 31, w + 25]$ | $...$ |
| 37 | $[37, 37, w + 3]$ | $...$ |
| 37 | $[37, 37, w + 33]$ | $...$ |
| 41 | $[41, 41, w]$ | $...$ |
| 41 | $[41, 41, w + 40]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -4w - 43]$ | $...$ |
| 53 | $[53, 53, 4w - 47]$ | $...$ |
| 59 | $[59, 59, -w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{552012708457686283}{528376897284126785048}e^{31} + \frac{3004537137713761113}{48034263389466071368}e^{29} + \frac{39509469442069108151}{24017131694733035684}e^{27} + \frac{13245287803622857833931}{528376897284126785048}e^{25} + \frac{32498090370053076007163}{132094224321031696262}e^{23} + \frac{216225910977371994755433}{132094224321031696262}e^{21} + \frac{1001199890589917198944937}{132094224321031696262}e^{19} + \frac{1631892497310405652085486}{66047112160515848131}e^{17} + \frac{7496603864115966210102113}{132094224321031696262}e^{15} + \frac{48086543850794033977798163}{528376897284126785048}e^{13} + \frac{52740612991850278822882277}{528376897284126785048}e^{11} + \frac{38163765387738923519893751}{528376897284126785048}e^{9} + \frac{8576130301473707729821385}{264188448642063392524}e^{7} + \frac{97976712093116979891233}{12008565847366517842}e^{5} + \frac{496198507825298990718379}{528376897284126785048}e^{3} + \frac{2146514291058826789852}{66047112160515848131}e$ |