Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $99$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} + 2x^{17} + 30x^{16} + 36x^{15} + 572x^{14} + 655x^{13} + 5454x^{12} + 4695x^{11} + 35080x^{10} + 25554x^{9} + 127413x^{8} + 27722x^{7} + 262459x^{6} + 16210x^{5} + 351257x^{4} - 115876x^{3} + 148288x^{2} + 17088x + 2304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 14]$ | $...$ |
| 19 | $[19, 19, w]$ | $...$ |
| 19 | $[19, 19, w + 18]$ | $...$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 37 | $[37, 37, w - 5]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -w - 10]$ | $...$ |
| 53 | $[53, 53, w - 11]$ | $...$ |
| 61 | $[61, 61, w + 15]$ | $...$ |
| 61 | $[61, 61, w + 45]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{901879756362826935306491803}{16388183099936711822646798008064}e^{17} + \frac{290243214111272349269710291}{2731363849989451970441133001344}e^{16} + \frac{13423087375819113571413553129}{8194091549968355911323399004032}e^{15} + \frac{7603453737805971723321808301}{4097045774984177955661699502016}e^{14} + \frac{127779534848306036422526412809}{4097045774984177955661699502016}e^{13} + \frac{551744116809822039677216203429}{16388183099936711822646798008064}e^{12} + \frac{2415407178929164285081663066399}{8194091549968355911323399004032}e^{11} + \frac{3832534401460584204106727277445}{16388183099936711822646798008064}e^{10} + \frac{858635071778059233780483524015}{455227308331575328406855500224}e^{9} + \frac{10209586734782254346708315709739}{8194091549968355911323399004032}e^{8} + \frac{110599709606426915618795322926159}{16388183099936711822646798008064}e^{7} + \frac{7271794025930535117678980979949}{8194091549968355911323399004032}e^{6} + \frac{225807750741922469122817278068673}{16388183099936711822646798008064}e^{5} - \frac{863907671871689531867244309649}{2731363849989451970441133001344}e^{4} + \frac{298795432460040935719076781712747}{16388183099936711822646798008064}e^{3} - \frac{316946436743339237481516560747}{37935609027631277367237958352}e^{2} + \frac{210384830512547997226474499467}{28451706770723458025428468764}e + \frac{8067585440867573865382141011}{9483902256907819341809489588}$ |
| $3$ | $[3, 3, w + 2]$ | $-\frac{901879756362826935306491803}{16388183099936711822646798008064}e^{17} - \frac{290243214111272349269710291}{2731363849989451970441133001344}e^{16} - \frac{13423087375819113571413553129}{8194091549968355911323399004032}e^{15} - \frac{7603453737805971723321808301}{4097045774984177955661699502016}e^{14} - \frac{127779534848306036422526412809}{4097045774984177955661699502016}e^{13} - \frac{551744116809822039677216203429}{16388183099936711822646798008064}e^{12} - \frac{2415407178929164285081663066399}{8194091549968355911323399004032}e^{11} - \frac{3832534401460584204106727277445}{16388183099936711822646798008064}e^{10} - \frac{858635071778059233780483524015}{455227308331575328406855500224}e^{9} - \frac{10209586734782254346708315709739}{8194091549968355911323399004032}e^{8} - \frac{110599709606426915618795322926159}{16388183099936711822646798008064}e^{7} - \frac{7271794025930535117678980979949}{8194091549968355911323399004032}e^{6} - \frac{225807750741922469122817278068673}{16388183099936711822646798008064}e^{5} + \frac{863907671871689531867244309649}{2731363849989451970441133001344}e^{4} - \frac{298795432460040935719076781712747}{16388183099936711822646798008064}e^{3} + \frac{316946436743339237481516560747}{37935609027631277367237958352}e^{2} - \frac{210384830512547997226474499467}{28451706770723458025428468764}e + \frac{1416316816040245476427348577}{9483902256907819341809489588}$ |