Base field 6.6.1416125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{3} + 4w]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 4x^{8} - 19x^{7} + 76x^{6} + 120x^{5} - 466x^{4} - 333x^{3} + 1068x^{2} + 388x - 632\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{513}{5167}e^{8} + \frac{553}{5167}e^{7} - \frac{15893}{5167}e^{6} - \frac{11661}{5167}e^{5} + \frac{146357}{5167}e^{4} + \frac{69154}{5167}e^{3} - \frac{444612}{5167}e^{2} - \frac{147929}{5167}e + \frac{286933}{5167}$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $-1$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ | $-\frac{345}{5167}e^{8} + \frac{1290}{5167}e^{7} + \frac{4645}{5167}e^{6} - \frac{18718}{5167}e^{5} - \frac{9440}{5167}e^{4} + \frac{71367}{5167}e^{3} - \frac{19261}{5167}e^{2} - \frac{78067}{5167}e + \frac{11568}{5167}$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $\phantom{-}\frac{1299}{5167}e^{8} - \frac{1712}{5167}e^{7} - \frac{29396}{5167}e^{6} + \frac{20964}{5167}e^{5} + \frac{210997}{5167}e^{4} - \frac{53810}{5167}e^{3} - \frac{540509}{5167}e^{2} - \frac{30144}{5167}e + \frac{300027}{5167}$ |
| 25 | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $\phantom{-}\frac{371}{10334}e^{8} + \frac{205}{5167}e^{7} - \frac{12783}{10334}e^{6} - \frac{3295}{5167}e^{5} + \frac{64309}{5167}e^{4} + \frac{17049}{5167}e^{3} - \frac{417479}{10334}e^{2} - \frac{54483}{5167}e + \frac{130773}{5167}$ |
| 29 | $[29, 29, -w^{3} + 4w + 1]$ | $-\frac{428}{5167}e^{8} + \frac{1825}{5167}e^{7} + \frac{4789}{5167}e^{6} - \frac{26561}{5167}e^{5} + \frac{4389}{5167}e^{4} + \frac{101746}{5167}e^{3} - \frac{103212}{5167}e^{2} - \frac{109983}{5167}e + \frac{122229}{5167}$ |
| 41 | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-\frac{1613}{10334}e^{8} + \frac{2117}{5167}e^{7} + \frac{29505}{10334}e^{6} - \frac{29364}{5167}e^{5} - \frac{81301}{5167}e^{4} + \frac{96944}{5167}e^{3} + \frac{310937}{10334}e^{2} - \frac{50902}{5167}e - \frac{23145}{5167}$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ | $\phantom{-}\frac{1299}{5167}e^{8} - \frac{1712}{5167}e^{7} - \frac{29396}{5167}e^{6} + \frac{20964}{5167}e^{5} + \frac{210997}{5167}e^{4} - \frac{53810}{5167}e^{3} - \frac{535342}{5167}e^{2} - \frac{30144}{5167}e + \frac{269025}{5167}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ | $\phantom{-}\frac{2698}{5167}e^{8} - \frac{2450}{5167}e^{7} - \frac{64257}{5167}e^{6} + \frac{22492}{5167}e^{5} + \frac{486884}{5167}e^{4} + \frac{15022}{5167}e^{3} - \frac{1311245}{5167}e^{2} - \frac{321770}{5167}e + \frac{756204}{5167}$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{3724}{5167}e^{8} + \frac{6511}{5167}e^{7} + \frac{80542}{5167}e^{6} - \frac{87009}{5167}e^{5} - \frac{557417}{5167}e^{4} + \frac{260030}{5167}e^{3} + \frac{1409918}{5167}e^{2} + \frac{33757}{5167}e - \frac{761700}{5167}$ |
| 61 | $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ | $\phantom{-}\frac{6249}{10334}e^{8} - \frac{5168}{5167}e^{7} - \frac{137153}{10334}e^{6} + \frac{66809}{5167}e^{5} + \frac{486947}{5167}e^{4} - \frac{182138}{5167}e^{3} - \frac{2556057}{10334}e^{2} - \frac{71921}{5167}e + \frac{723347}{5167}$ |
| 64 | $[64, 2, -2]$ | $-\frac{2075}{10334}e^{8} + \frac{4104}{5167}e^{7} + \frac{29435}{10334}e^{6} - \frac{59285}{5167}e^{5} - \frac{46735}{5167}e^{4} + \frac{206643}{5167}e^{3} + \frac{40363}{10334}e^{2} - \frac{125099}{5167}e + \frac{37259}{5167}$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $-\frac{4241}{5167}e^{8} + \frac{5299}{5167}e^{7} + \frac{97687}{5167}e^{6} - \frac{60723}{5167}e^{5} - \frac{722904}{5167}e^{4} + \frac{93171}{5167}e^{3} + \frac{1934837}{5167}e^{2} + \frac{378984}{5167}e - \frac{1101382}{5167}$ |
| 71 | $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ | $\phantom{-}\frac{3855}{5167}e^{8} - \frac{4305}{5167}e^{7} - \frac{90543}{5167}e^{6} + \frac{48527}{5167}e^{5} + \frac{680142}{5167}e^{4} - \frac{73844}{5167}e^{3} - \frac{1834955}{5167}e^{2} - \frac{302617}{5167}e + \frac{1092848}{5167}$ |
| 79 | $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ | $\phantom{-}\frac{3484}{5167}e^{8} - \frac{4715}{5167}e^{7} - \frac{77760}{5167}e^{6} + \frac{55117}{5167}e^{5} + \frac{551524}{5167}e^{4} - \frac{107942}{5167}e^{3} - \frac{1407142}{5167}e^{2} - \frac{193651}{5167}e + \frac{769298}{5167}$ |
| 79 | $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ | $\phantom{-}\frac{1323}{5167}e^{8} - \frac{2925}{5167}e^{7} - \frac{26574}{5167}e^{6} + \frac{41721}{5167}e^{5} + \frac{165600}{5167}e^{4} - \frac{149624}{5167}e^{3} - \frac{360975}{5167}e^{2} + \frac{93319}{5167}e + \frac{141157}{5167}$ |
| 89 | $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ | $-\frac{1984}{5167}e^{8} + \frac{3824}{5167}e^{7} + \frac{42288}{5167}e^{6} - \frac{52138}{5167}e^{5} - \frac{291220}{5167}e^{4} + \frac{159790}{5167}e^{3} + \frac{749084}{5167}e^{2} - \frac{3172}{5167}e - \frac{431844}{5167}$ |
| 109 | $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ | $-\frac{2150}{5167}e^{8} + \frac{4894}{5167}e^{7} + \frac{42576}{5167}e^{6} - \frac{67824}{5167}e^{5} - \frac{263562}{5167}e^{4} + \frac{220548}{5167}e^{3} + \frac{581182}{5167}e^{2} - \frac{67004}{5167}e - \frac{210522}{5167}$ |
| 109 | $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ | $\phantom{-}\frac{965}{5167}e^{8} - \frac{2485}{5167}e^{7} - \frac{17860}{5167}e^{6} + \frac{35657}{5167}e^{5} + \frac{96571}{5167}e^{4} - \frac{128406}{5167}e^{3} - \frac{161866}{5167}e^{2} + \frac{95851}{5167}e + \frac{667}{5167}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{3} + 4w]$ | $1$ |