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: | $7$ |
| 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:
| \(x^{7} + 2x^{6} - 12x^{5} - 20x^{4} + 39x^{3} + 53x^{2} - 38x - 41\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{37}{88}e^{6} + \frac{75}{88}e^{5} - \frac{373}{88}e^{4} - \frac{55}{8}e^{3} + \frac{353}{44}e^{2} + \frac{779}{88}e - \frac{103}{88}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{9}{88}e^{6} + \frac{23}{88}e^{5} - \frac{105}{88}e^{4} - \frac{19}{8}e^{3} + \frac{181}{44}e^{2} + \frac{375}{88}e - \frac{339}{88}$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{1}{44}e^{6} + \frac{27}{44}e^{5} + \frac{47}{44}e^{4} - \frac{23}{4}e^{3} - \frac{217}{22}e^{2} + \frac{423}{44}e + \frac{593}{44}$ |
| 11 | $[11, 11, w + 9]$ | $-\frac{15}{44}e^{6} - \frac{53}{44}e^{5} + \frac{87}{44}e^{4} + \frac{41}{4}e^{3} + \frac{131}{22}e^{2} - \frac{713}{44}e - \frac{799}{44}$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{45}{88}e^{6} - \frac{115}{88}e^{5} + \frac{437}{88}e^{4} + \frac{87}{8}e^{3} - \frac{465}{44}e^{2} - \frac{1347}{88}e + \frac{375}{88}$ |
| 17 | $[17, 17, w + 14]$ | $\phantom{-}\frac{75}{88}e^{6} + \frac{133}{88}e^{5} - \frac{787}{88}e^{4} - \frac{97}{8}e^{3} + \frac{863}{44}e^{2} + \frac{1541}{88}e - \frac{625}{88}$ |
| 19 | $[19, 19, w]$ | $\phantom{-}\frac{4}{11}e^{6} + \frac{9}{11}e^{5} - \frac{32}{11}e^{4} - 6e^{3} + \frac{13}{11}e^{2} + \frac{64}{11}e + \frac{62}{11}$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{10}{11}e^{6} - \frac{17}{11}e^{5} + \frac{102}{11}e^{4} + 12e^{3} - \frac{203}{11}e^{2} - \frac{182}{11}e + \frac{32}{11}$ |
| 37 | $[37, 37, -w - 4]$ | $-\frac{35}{88}e^{6} - \frac{21}{88}e^{5} + \frac{379}{88}e^{4} + \frac{9}{8}e^{3} - \frac{303}{44}e^{2} - \frac{21}{88}e - \frac{647}{88}$ |
| 37 | $[37, 37, w - 5]$ | $-\frac{67}{88}e^{6} - \frac{181}{88}e^{5} + \frac{635}{88}e^{4} + \frac{137}{8}e^{3} - \frac{575}{44}e^{2} - \frac{1941}{88}e + \frac{89}{88}$ |
| 43 | $[43, 43, w + 16]$ | $-\frac{35}{44}e^{6} - \frac{65}{44}e^{5} + \frac{379}{44}e^{4} + \frac{49}{4}e^{3} - \frac{457}{22}e^{2} - \frac{769}{44}e + \frac{453}{44}$ |
| 43 | $[43, 43, w + 26]$ | $-\frac{1}{4}e^{6} - \frac{11}{4}e^{5} - \frac{7}{4}e^{4} + \frac{105}{4}e^{3} + \frac{53}{2}e^{2} - \frac{187}{4}e - \frac{153}{4}$ |
| 49 | $[49, 7, -7]$ | $-\frac{19}{88}e^{6} - \frac{117}{88}e^{5} - \frac{13}{88}e^{4} + \frac{97}{8}e^{3} + \frac{625}{44}e^{2} - \frac{1877}{88}e - \frac{2159}{88}$ |
| 53 | $[53, 53, -w - 10]$ | $\phantom{-}\frac{1}{88}e^{6} - \frac{17}{88}e^{5} - \frac{41}{88}e^{4} + \frac{21}{8}e^{3} + \frac{113}{44}e^{2} - \frac{809}{88}e - \frac{243}{88}$ |
| 53 | $[53, 53, w - 11]$ | $-\frac{3}{88}e^{6} + \frac{51}{88}e^{5} + \frac{123}{88}e^{4} - \frac{47}{8}e^{3} - \frac{339}{44}e^{2} + \frac{843}{88}e + \frac{377}{88}$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}\frac{53}{88}e^{6} - \frac{21}{88}e^{5} - \frac{765}{88}e^{4} + \frac{33}{8}e^{3} + \frac{1413}{44}e^{2} - \frac{813}{88}e - \frac{2495}{88}$ |
| 61 | $[61, 61, w + 45]$ | $\phantom{-}\frac{5}{88}e^{6} + \frac{91}{88}e^{5} + \frac{147}{88}e^{4} - \frac{79}{8}e^{3} - \frac{843}{44}e^{2} + \frac{1763}{88}e + \frac{2833}{88}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $3$ | $[3, 3, w + 2]$ | $1$ |