Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, w^{2} - w - 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 4x^{9} - 11x^{8} + 54x^{7} + 25x^{6} - 223x^{5} + 22x^{4} + 339x^{3} - 80x^{2} - 165x + 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{221}{751}e^{9} - \frac{678}{751}e^{8} - \frac{3029}{751}e^{7} + \frac{8713}{751}e^{6} + \frac{13684}{751}e^{5} - \frac{31981}{751}e^{4} - \frac{27847}{751}e^{3} + \frac{35947}{751}e^{2} + \frac{22508}{751}e - \frac{6646}{751}$ |
| 8 | $[8, 2, 2]$ | $-\frac{364}{751}e^{9} + \frac{940}{751}e^{8} + \frac{5254}{751}e^{7} - \frac{12142}{751}e^{6} - \frac{25454}{751}e^{5} + \frac{44767}{751}e^{4} + \frac{54215}{751}e^{3} - \frac{48737}{751}e^{2} - \frac{43080}{751}e + \frac{6352}{751}$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $-\frac{170}{751}e^{9} + \frac{406}{751}e^{8} + \frac{2330}{751}e^{7} - \frac{5027}{751}e^{6} - \frac{10064}{751}e^{5} + \frac{17033}{751}e^{4} + \frac{17608}{751}e^{3} - \frac{15520}{751}e^{2} - \frac{11768}{751}e + \frac{1184}{751}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{230}{751}e^{9} + \frac{726}{751}e^{8} + \frac{3064}{751}e^{7} - \frac{9496}{751}e^{6} - \frac{12865}{751}e^{5} + \frac{35900}{751}e^{4} + \frac{22674}{751}e^{3} - \frac{41363}{751}e^{2} - \frac{15568}{751}e + \frac{8140}{751}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{582}{751}e^{9} - \frac{1602}{751}e^{8} - \frac{8021}{751}e^{7} + \frac{20594}{751}e^{6} + \frac{35656}{751}e^{5} - \frac{75692}{751}e^{4} - \frac{67014}{751}e^{3} + \frac{84631}{751}e^{2} + \frac{45872}{751}e - \frac{14002}{751}$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{155}{751}e^{9} - \frac{326}{751}e^{8} - \frac{2522}{751}e^{7} + \frac{4473}{751}e^{6} + \frac{14433}{751}e^{5} - \frac{18512}{751}e^{4} - \frac{35492}{751}e^{3} + \frac{24267}{751}e^{2} + \frac{28842}{751}e - \frac{3951}{751}$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $-\frac{1116}{751}e^{9} + \frac{2948}{751}e^{8} + \frac{16356}{751}e^{7} - \frac{38514}{751}e^{6} - \frac{80937}{751}e^{5} + \frac{145002}{751}e^{4} + \frac{173383}{751}e^{3} - \frac{165410}{751}e^{2} - \frac{131511}{751}e + \frac{29799}{751}$ |
| 19 | $[19, 19, -w^{2} + 3w + 2]$ | $-\frac{300}{751}e^{9} + \frac{849}{751}e^{8} + \frac{4421}{751}e^{7} - \frac{11080}{751}e^{6} - \frac{22266}{751}e^{5} + \frac{41014}{751}e^{4} + \frac{49362}{751}e^{3} - \frac{42850}{751}e^{2} - \frac{38526}{751}e + \frac{3238}{751}$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{269}{751}e^{9} - \frac{934}{751}e^{8} - \frac{3466}{751}e^{7} + \frac{12138}{751}e^{6} + \frac{13822}{751}e^{5} - \frac{45122}{751}e^{4} - \frac{23789}{751}e^{3} + \frac{50313}{751}e^{2} + \frac{17287}{751}e - \frac{6353}{751}$ |
| 23 | $[23, 23, -w + 4]$ | $-\frac{991}{751}e^{9} + \frac{2782}{751}e^{8} + \frac{14201}{751}e^{7} - \frac{35900}{751}e^{6} - \frac{68280}{751}e^{5} + \frac{131793}{751}e^{4} + \frac{143428}{751}e^{3} - \frac{143175}{751}e^{2} - \frac{107573}{751}e + \frac{20314}{751}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $-\frac{24}{751}e^{9} + \frac{128}{751}e^{8} + \frac{594}{751}e^{7} - \frac{2088}{751}e^{6} - \frac{5326}{751}e^{5} + \frac{10701}{751}e^{4} + \frac{18999}{751}e^{3} - \frac{18448}{751}e^{2} - \frac{19544}{751}e + \frac{6988}{751}$ |
| 43 | $[43, 43, w^{2} - 3w - 3]$ | $\phantom{-}\frac{595}{751}e^{9} - \frac{1421}{751}e^{8} - \frac{8906}{751}e^{7} + \frac{18721}{751}e^{6} + \frac{44987}{751}e^{5} - \frac{72007}{751}e^{4} - \frac{96174}{751}e^{3} + \frac{85862}{751}e^{2} + \frac{71228}{751}e - \frac{13156}{751}$ |
| 49 | $[49, 7, w^{2} - 6]$ | $\phantom{-}\frac{1594}{751}e^{9} - \frac{4496}{751}e^{8} - \frac{22554}{751}e^{7} + \frac{58321}{751}e^{6} + \frac{105780}{751}e^{5} - \frac{216379}{751}e^{4} - \frac{215144}{751}e^{3} + \frac{238691}{751}e^{2} + \frac{159281}{751}e - \frac{32545}{751}$ |
| 53 | $[53, 53, 2w - 5]$ | $-\frac{1358}{751}e^{9} + \frac{3738}{751}e^{8} + \frac{19717}{751}e^{7} - \frac{49054}{751}e^{6} - \frac{95714}{751}e^{5} + \frac{185877}{751}e^{4} + \frac{198422}{751}e^{3} - \frac{213744}{751}e^{2} - \frac{145586}{751}e + \frac{37678}{751}$ |
| 61 | $[61, 61, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{1431}{751}e^{9} - \frac{3877}{751}e^{8} - \frac{21336}{751}e^{7} + \frac{50899}{751}e^{6} + \frac{108597}{751}e^{5} - \frac{192798}{751}e^{4} - \frac{239407}{751}e^{3} + \frac{222043}{751}e^{2} + \frac{183754}{751}e - \frac{38531}{751}$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}\frac{103}{751}e^{9} - \frac{299}{751}e^{8} - \frac{1986}{751}e^{7} + \frac{4455}{751}e^{6} + \frac{13908}{751}e^{5} - \frac{19734}{751}e^{4} - \frac{41265}{751}e^{3} + \frac{25351}{751}e^{2} + \frac{41570}{751}e - \frac{4331}{751}$ |
| 73 | $[73, 73, 2w^{2} - 5w - 5]$ | $\phantom{-}\frac{1855}{751}e^{9} - \frac{5137}{751}e^{8} - \frac{26573}{751}e^{7} + \frac{66759}{751}e^{6} + \frac{127089}{751}e^{5} - \frac{248171}{751}e^{4} - \frac{262640}{751}e^{3} + \frac{271840}{751}e^{2} + \frac{190831}{751}e - \frac{33815}{751}$ |
| 83 | $[83, 83, w^{2} - w - 9]$ | $\phantom{-}\frac{1105}{751}e^{9} - \frac{2639}{751}e^{8} - \frac{16647}{751}e^{7} + \frac{34553}{751}e^{6} + \frac{84942}{751}e^{5} - \frac{131367}{751}e^{4} - \frac{183544}{751}e^{3} + \frac{154952}{751}e^{2} + \frac{137323}{751}e - \frac{30226}{751}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, w^{2} - w - 3]$ | $-1$ |