Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,w - 8]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 23x^{8} + 165x^{6} + 398x^{4} + 268x^{2} + 49\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{3}{2926}e^{9} + \frac{59}{1463}e^{7} + \frac{1447}{2926}e^{5} + \frac{6297}{2926}e^{3} + \frac{7097}{2926}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{3}{2926}e^{9} + \frac{59}{1463}e^{7} + \frac{1447}{2926}e^{5} + \frac{6297}{2926}e^{3} + \frac{7097}{2926}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w + 15]$ | $-\frac{7}{1254}e^{8} - \frac{68}{627}e^{6} - \frac{311}{1254}e^{4} + \frac{1233}{418}e^{2} + \frac{4619}{1254}$ |
| 7 | $[7, 7, -2w - 15]$ | $-\frac{29}{627}e^{8} - \frac{653}{627}e^{6} - \frac{4513}{627}e^{4} - \frac{3222}{209}e^{2} - \frac{3257}{627}$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{293}{2926}e^{9} - \frac{3324}{1463}e^{7} - \frac{45741}{2926}e^{5} - \frac{94179}{2926}e^{3} - \frac{22111}{2926}e$ |
| 11 | $[11, 11, w + 6]$ | $\phantom{-}\frac{9}{38}e^{9} + \frac{101}{19}e^{7} + \frac{1377}{38}e^{5} + \frac{2893}{38}e^{3} + \frac{1151}{38}e$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{223}{8778}e^{9} - \frac{2435}{4389}e^{7} - \frac{30509}{8778}e^{5} - \frac{13627}{2926}e^{3} + \frac{65459}{8778}e$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}\frac{725}{4389}e^{9} + \frac{16325}{4389}e^{7} + \frac{112198}{4389}e^{5} + \frac{80550}{1463}e^{3} + \frac{98981}{4389}e$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}\frac{37}{418}e^{8} + \frac{449}{209}e^{6} + \frac{6839}{418}e^{4} + \frac{17053}{418}e^{2} + \frac{8249}{418}$ |
| 23 | $[23, 23, -w + 9]$ | $-\frac{24}{209}e^{8} - \frac{526}{209}e^{6} - \frac{3425}{209}e^{4} - \frac{6486}{209}e^{2} - \frac{2018}{209}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{130}{627}e^{8} + \frac{2884}{627}e^{6} + \frac{19301}{627}e^{4} + \frac{12930}{209}e^{2} + \frac{12568}{627}$ |
| 29 | $[29, 29, w]$ | $\phantom{-}\frac{403}{2926}e^{9} + \frac{4512}{1463}e^{7} + \frac{61735}{2926}e^{5} + \frac{134879}{2926}e^{3} + \frac{76539}{2926}e$ |
| 37 | $[37, 37, w + 13]$ | $\phantom{-}\frac{1258}{4389}e^{9} + \frac{28024}{4389}e^{7} + \frac{187382}{4389}e^{5} + \frac{123322}{1463}e^{3} + \frac{109504}{4389}e$ |
| 37 | $[37, 37, w + 24]$ | $\phantom{-}\frac{167}{627}e^{9} + \frac{3782}{627}e^{7} + \frac{26140}{627}e^{5} + \frac{18684}{209}e^{3} + \frac{21026}{627}e$ |
| 43 | $[43, 43, w + 12]$ | $-\frac{2293}{8778}e^{9} - \frac{25589}{4389}e^{7} - \frac{344255}{8778}e^{5} - \frac{233017}{2926}e^{3} - \frac{258133}{8778}e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{197}{462}e^{9} - \frac{2206}{231}e^{7} - \frac{29929}{462}e^{5} - \frac{20589}{154}e^{3} - \frac{20771}{462}e$ |
| 61 | $[61, 61, w + 27]$ | $-\frac{383}{1463}e^{9} - \frac{8725}{1463}e^{7} - \frac{61354}{1463}e^{5} - \frac{139715}{1463}e^{3} - \frac{71165}{1463}e$ |
| 61 | $[61, 61, w + 34]$ | $-\frac{696}{1463}e^{9} - \frac{15672}{1463}e^{7} - \frac{107476}{1463}e^{5} - \frac{229058}{1463}e^{3} - \frac{92798}{1463}e$ |
| 71 | $[71, 71, 12w - 91]$ | $\phantom{-}\frac{147}{418}e^{8} + \frac{1637}{209}e^{6} + \frac{21997}{418}e^{4} + \frac{45213}{418}e^{2} + \frac{17115}{418}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w]$ | $-\frac{3}{2926}e^{9} - \frac{59}{1463}e^{7} - \frac{1447}{2926}e^{5} - \frac{6297}{2926}e^{3} - \frac{7097}{2926}e$ |
| $3$ | $[3,3,-w + 2]$ | $-\frac{3}{2926}e^{9} - \frac{59}{1463}e^{7} - \frac{1447}{2926}e^{5} - \frac{6297}{2926}e^{3} - \frac{7097}{2926}e$ |