Base field 6.6.592661.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[37, 37, w^{4} - 5w^{2} + w + 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 6x^{6} - 21x^{5} + 160x^{4} - 31x^{3} - 594x^{2} - 12x + 414\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{5} - 5w^{3} + 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{3} + 3w]$ | $\phantom{-}\frac{10}{5079}e^{6} - \frac{23}{1693}e^{5} + \frac{120}{1693}e^{4} + \frac{1276}{5079}e^{3} - \frac{13648}{5079}e^{2} + \frac{2453}{1693}e + \frac{11127}{1693}$ |
| 25 | $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{281}{5079}e^{6} + \frac{477}{1693}e^{5} + \frac{1707}{1693}e^{4} - \frac{33824}{5079}e^{3} + \frac{26963}{5079}e^{2} + \frac{14197}{1693}e - \frac{13177}{1693}$ |
| 31 | $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ | $-\frac{239}{5079}e^{6} + \frac{719}{1693}e^{5} + \frac{518}{1693}e^{4} - \frac{52844}{5079}e^{3} + \frac{88490}{5079}e^{2} + \frac{34319}{1693}e - \frac{32132}{1693}$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{110}{5079}e^{6} - \frac{253}{1693}e^{5} - \frac{373}{1693}e^{4} + \frac{19115}{5079}e^{3} - \frac{33311}{5079}e^{2} - \frac{13649}{1693}e + \frac{20817}{1693}$ |
| 37 | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $-1$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $\phantom{-}\frac{29}{5079}e^{6} - \frac{236}{1693}e^{5} + \frac{348}{1693}e^{4} + \frac{15890}{5079}e^{3} - \frac{40595}{5079}e^{2} - \frac{2875}{1693}e + \frac{20248}{1693}$ |
| 47 | $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ | $-\frac{1133}{10158}e^{6} + \frac{1049}{1693}e^{5} + \frac{3360}{1693}e^{4} - \frac{153713}{10158}e^{3} + \frac{63115}{5079}e^{2} + \frac{44982}{1693}e - \frac{30430}{1693}$ |
| 49 | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $-e + 1$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ | $-\frac{43}{1693}e^{6} + \frac{466}{1693}e^{5} + \frac{145}{1693}e^{4} - \frac{11243}{1693}e^{3} + \frac{20086}{1693}e^{2} + \frac{18977}{1693}e - \frac{26552}{1693}$ |
| 59 | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $-\frac{37}{10158}e^{6} + \frac{593}{3386}e^{5} - \frac{2137}{3386}e^{4} - \frac{20645}{5079}e^{3} + \frac{85181}{5079}e^{2} + \frac{3673}{1693}e - \frac{33875}{1693}$ |
| 61 | $[61, 61, w^{3} - w^{2} - 3w]$ | $\phantom{-}\frac{43}{1693}e^{6} - \frac{466}{1693}e^{5} - \frac{145}{1693}e^{4} + \frac{11243}{1693}e^{3} - \frac{20086}{1693}e^{2} - \frac{18977}{1693}e + \frac{29938}{1693}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{35}{5079}e^{6} - \frac{161}{3386}e^{5} - \frac{853}{3386}e^{4} + \frac{14011}{10158}e^{3} + \frac{13180}{5079}e^{2} - \frac{12577}{1693}e - \frac{9306}{1693}$ |
| 67 | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $\phantom{-}\frac{307}{10158}e^{6} - \frac{607}{1693}e^{5} + \frac{149}{1693}e^{4} + \frac{90979}{10158}e^{3} - \frac{91664}{5079}e^{2} - \frac{35738}{1693}e + \frac{41031}{1693}$ |
| 67 | $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ | $-\frac{953}{10158}e^{6} + \frac{842}{1693}e^{5} + \frac{2747}{1693}e^{4} - \frac{120587}{10158}e^{3} + \frac{57100}{5079}e^{2} + \frac{29813}{1693}e - \frac{31867}{1693}$ |
| 73 | $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ | $\phantom{-}\frac{149}{5079}e^{6} - \frac{512}{1693}e^{5} + \frac{95}{1693}e^{4} + \frac{36281}{5079}e^{3} - \frac{87554}{5079}e^{2} - \frac{17457}{1693}e + \frac{52192}{1693}$ |
| 73 | $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ | $\phantom{-}\frac{401}{3386}e^{6} - \frac{2259}{3386}e^{5} - \frac{7573}{3386}e^{4} + \frac{27954}{1693}e^{3} - \frac{16645}{1693}e^{2} - \frac{57559}{1693}e + \frac{21124}{1693}$ |
| 83 | $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ | $-\frac{213}{1693}e^{6} + \frac{1639}{1693}e^{5} + \frac{2490}{1693}e^{4} - \frac{39707}{1693}e^{3} + \frac{54021}{1693}e^{2} + \frac{69946}{1693}e - \frac{67506}{1693}$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ | $\phantom{-}\frac{127}{1693}e^{6} - \frac{707}{1693}e^{5} - \frac{2200}{1693}e^{4} + \frac{17221}{1693}e^{3} - \frac{13849}{1693}e^{2} - \frac{31992}{1693}e + \frac{11016}{1693}$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ | $-\frac{361}{5079}e^{6} + \frac{661}{1693}e^{5} + \frac{2440}{1693}e^{4} - \frac{49111}{5079}e^{3} + \frac{19330}{5079}e^{2} + \frac{36898}{1693}e + \frac{1080}{1693}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $1$ |