Base field 4.4.14197.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{3} - w^{2} - 5w]$ |
| Dimension: | $12$ |
| 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:
| \(x^{12} - 58x^{10} + 1066x^{8} - 6754x^{6} + 17184x^{4} - 15824x^{2} + 1568\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w - 2]$ | $\phantom{-}\frac{102727}{19959408}e^{11} - \frac{950449}{3326568}e^{9} + \frac{47627351}{9979704}e^{7} - \frac{25182447}{1108856}e^{5} + \frac{12113845}{415821}e^{3} + \frac{3795970}{1247463}e$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-\frac{71075}{29939112}e^{11} + \frac{661331}{4989852}e^{9} - \frac{33675037}{14969556}e^{7} + \frac{6389161}{554428}e^{5} - \frac{27311131}{1247463}e^{3} + \frac{60124304}{3742389}e$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{2627}{4277016}e^{11} - \frac{45349}{1425672}e^{9} + \frac{237004}{534627}e^{7} - \frac{12126}{19801}e^{5} - \frac{4650761}{712836}e^{3} + \frac{7628041}{534627}e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{4327}{1425672}e^{10} - \frac{10216}{59403}e^{8} + \frac{2137781}{712836}e^{6} - \frac{1286597}{79204}e^{4} + \frac{3360067}{118806}e^{2} - \frac{1368655}{178209}$ |
| 17 | $[17, 17, w^{3} - w^{2} - 5w]$ | $-1$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 6w]$ | $-\frac{1763}{475224}e^{10} + \frac{4167}{19801}e^{8} - \frac{875167}{237612}e^{6} + \frac{1592555}{79204}e^{4} - \frac{1323947}{39602}e^{2} + \frac{408611}{59403}$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}\frac{11183}{3742389}e^{11} - \frac{1640105}{9979704}e^{9} + \frac{40311149}{14969556}e^{7} - \frac{6728689}{554428}e^{5} + \frac{76689197}{4989852}e^{3} - \frac{2985628}{3742389}e$ |
| 29 | $[29, 29, w^{3} - 5w]$ | $\phantom{-}\frac{35951}{9979704}e^{11} - \frac{163129}{831642}e^{9} + \frac{15649087}{4989852}e^{7} - \frac{7068217}{554428}e^{5} + \frac{7355645}{831642}e^{3} + \frac{15556090}{1247463}e$ |
| 31 | $[31, 31, w^{3} - 6w - 1]$ | $-\frac{234625}{59878224}e^{11} + \frac{2216461}{9979704}e^{9} - \frac{116337605}{29939112}e^{7} + \frac{23824335}{1108856}e^{5} - \frac{105238397}{2494926}e^{3} + \frac{87919886}{3742389}e$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-\frac{138923}{19959408}e^{11} + \frac{327323}{831642}e^{9} - \frac{68382721}{9979704}e^{7} + \frac{41361381}{1108856}e^{5} - \frac{116169239}{1663284}e^{3} + \frac{42994030}{1247463}e$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}\frac{64333}{4277016}e^{10} - \frac{596287}{712836}e^{8} + \frac{30033161}{2138508}e^{6} - \frac{5422967}{79204}e^{4} + \frac{18186476}{178209}e^{2} - \frac{9647668}{534627}$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $\phantom{-}\frac{34115}{9979704}e^{11} - \frac{159841}{831642}e^{9} + \frac{16467007}{4989852}e^{7} - \frac{9475269}{554428}e^{5} + \frac{21834143}{831642}e^{3} + \frac{1834474}{1247463}e$ |
| 37 | $[37, 37, w^{3} - 7w - 4]$ | $-\frac{9605}{712836}e^{10} + \frac{89405}{118806}e^{8} - \frac{2269556}{178209}e^{6} + \frac{2501781}{39602}e^{4} - \frac{5384003}{59403}e^{2} + \frac{1473565}{178209}$ |
| 37 | $[37, 37, w^{2} - 3]$ | $-\frac{162815}{59878224}e^{11} + \frac{1457375}{9979704}e^{9} - \frac{67343719}{29939112}e^{7} + \frac{8324457}{1108856}e^{5} + \frac{12610055}{2494926}e^{3} - \frac{102104012}{3742389}e$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $\phantom{-}\frac{75437}{59878224}e^{11} - \frac{353425}{4989852}e^{9} + \frac{36542287}{29939112}e^{7} - \frac{7225469}{1108856}e^{5} + \frac{62327915}{4989852}e^{3} - \frac{12612505}{3742389}e$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}\frac{12469}{2138508}e^{10} - \frac{113899}{356418}e^{8} + \frac{2776966}{534627}e^{6} - \frac{901505}{39602}e^{4} + \frac{4749187}{178209}e^{2} + \frac{1111501}{534627}$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 5w - 4]$ | $-\frac{235}{712836}e^{10} + \frac{3107}{237612}e^{8} - \frac{9845}{356418}e^{6} - \frac{56098}{19801}e^{4} + \frac{1701421}{118806}e^{2} - \frac{2018221}{178209}$ |
| 53 | $[53, 53, w^{3} - 6w]$ | $-\frac{35339}{3326568}e^{11} + \frac{162033}{277214}e^{9} - \frac{15921727}{1663284}e^{7} + \frac{23611703}{554428}e^{5} - \frac{12181811}{277214}e^{3} - \frac{10566397}{415821}e$ |
| 61 | $[61, 61, w^{3} - w^{2} - 7w - 2]$ | $-\frac{36961}{4277016}e^{10} + \frac{170891}{356418}e^{8} - \frac{17147405}{2138508}e^{6} + \frac{3074165}{79204}e^{4} - \frac{21316813}{356418}e^{2} + \frac{10698163}{534627}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{3} - w^{2} - 5w]$ | $1$ |