Base field 6.6.1995125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{4} + 4w^{3} - 9w]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} + 11x^{7} + 14x^{6} - 146x^{5} - 195x^{4} + 837x^{3} + 331x^{2} - 1971x + 1125\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $\phantom{-}\frac{45020}{196557}e^{7} + \frac{552091}{196557}e^{6} + \frac{1329043}{196557}e^{5} - \frac{4874152}{196557}e^{4} - \frac{4933829}{65519}e^{3} + \frac{6408400}{65519}e^{2} + \frac{38042696}{196557}e - \frac{13950228}{65519}$ |
| 11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{5823}{65519}e^{7} - \frac{69856}{65519}e^{6} - \frac{152297}{65519}e^{5} + \frac{688235}{65519}e^{4} + \frac{1825193}{65519}e^{3} - \frac{2897301}{65519}e^{2} - \frac{4854594}{65519}e + \frac{5906622}{65519}$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $-\frac{7390}{196557}e^{7} - \frac{86303}{196557}e^{6} - \frac{177776}{196557}e^{5} + \frac{798866}{196557}e^{4} + \frac{609529}{65519}e^{3} - \frac{1102667}{65519}e^{2} - \frac{4194847}{196557}e + \frac{1860306}{65519}$ |
| 19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $-\frac{10079}{196557}e^{7} - \frac{123265}{196557}e^{6} - \frac{279115}{196557}e^{5} + \frac{1265839}{196557}e^{4} + \frac{1215664}{65519}e^{3} - \frac{1794634}{65519}e^{2} - \frac{10368935}{196557}e + \frac{3849759}{65519}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $-\frac{32497}{196557}e^{7} - \frac{396986}{196557}e^{6} - \frac{928949}{196557}e^{5} + \frac{3696587}{196557}e^{4} + \frac{3602352}{65519}e^{3} - \frac{5110169}{65519}e^{2} - \frac{29158579}{196557}e + \frac{11000292}{65519}$ |
| 29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $-\frac{57784}{196557}e^{7} - \frac{699398}{196557}e^{6} - \frac{1593488}{196557}e^{5} + \frac{6581051}{196557}e^{4} + \frac{6206623}{65519}e^{3} - \frac{8896993}{65519}e^{2} - \frac{49644628}{196557}e + \frac{18797190}{65519}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $\phantom{-}\frac{7553}{65519}e^{7} + \frac{88641}{65519}e^{6} + \frac{171395}{65519}e^{5} - \frac{986694}{65519}e^{4} - \frac{2328005}{65519}e^{3} + \frac{4440378}{65519}e^{2} + \frac{6776039}{65519}e - \frac{9113078}{65519}$ |
| 29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $\phantom{-}1$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $-\frac{4705}{196557}e^{7} - \frac{62261}{196557}e^{6} - \frac{192446}{196557}e^{5} + \frac{357806}{196557}e^{4} + \frac{552399}{65519}e^{3} - \frac{474227}{65519}e^{2} - \frac{3748078}{196557}e + \frac{1452774}{65519}$ |
| 41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $\phantom{-}\frac{67318}{196557}e^{7} + \frac{831326}{196557}e^{6} + \frac{2036633}{196557}e^{5} - \frac{7313738}{196557}e^{4} - \frac{7623231}{65519}e^{3} + \frac{9587138}{65519}e^{2} + \frac{59751943}{196557}e - \frac{21472001}{65519}$ |
| 59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $\phantom{-}\frac{1691}{65519}e^{7} + \frac{23853}{65519}e^{6} + \frac{83732}{65519}e^{5} - \frac{127706}{65519}e^{4} - \frac{873305}{65519}e^{3} + \frac{159925}{65519}e^{2} + \frac{2213488}{65519}e - \frac{1275250}{65519}$ |
| 61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $-\frac{22602}{65519}e^{7} - \frac{278370}{65519}e^{6} - \frac{679209}{65519}e^{5} + \frac{2443404}{65519}e^{4} + \frac{7641423}{65519}e^{3} - \frac{9409633}{65519}e^{2} - \frac{19908242}{65519}e + \frac{20988756}{65519}$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $\phantom{-}\frac{7532}{65519}e^{7} + \frac{86330}{65519}e^{6} + \frac{135639}{65519}e^{5} - \frac{1161866}{65519}e^{4} - \frac{2411583}{65519}e^{3} + \frac{5520056}{65519}e^{2} + \frac{7648962}{65519}e - \frac{10814916}{65519}$ |
| 61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $\phantom{-}\frac{39827}{196557}e^{7} + \frac{486046}{196557}e^{6} + \frac{1135603}{196557}e^{5} - \frac{4499872}{196557}e^{4} - \frac{4363238}{65519}e^{3} + \frac{6111678}{65519}e^{2} + \frac{34518392}{196557}e - \frac{13308294}{65519}$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $-\frac{102497}{196557}e^{7} - \frac{1242664}{196557}e^{6} - \frac{2814766}{196557}e^{5} + \frac{11972482}{196557}e^{4} + \frac{11214934}{65519}e^{3} - \frac{16572102}{65519}e^{2} - \frac{91204208}{196557}e + \frac{35378828}{65519}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1751}{65519}e^{7} + \frac{21096}{65519}e^{6} + \frac{54854}{65519}e^{5} - \frac{123287}{65519}e^{4} - \frac{419234}{65519}e^{3} + \frac{397880}{65519}e^{2} + \frac{917484}{65519}e - \frac{1111504}{65519}$ |
| 79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $\phantom{-}\frac{114779}{196557}e^{7} + \frac{1405567}{196557}e^{6} + \frac{3350509}{196557}e^{5} - \frac{12620713}{196557}e^{4} - \frac{12605094}{65519}e^{3} + \frac{16745490}{65519}e^{2} + \frac{98353295}{196557}e - \frac{36562776}{65519}$ |
| 89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $\phantom{-}\frac{12542}{65519}e^{7} + \frac{150956}{65519}e^{6} + \frac{345086}{65519}e^{5} - \frac{1349791}{65519}e^{4} - \frac{3775295}{65519}e^{3} + \frac{5242206}{65519}e^{2} + \frac{9307991}{65519}e - \frac{10770077}{65519}$ |
| 101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $-\frac{30113}{196557}e^{7} - \frac{362389}{196557}e^{6} - \frac{779092}{196557}e^{5} + \frac{3780442}{196557}e^{4} + \frac{3400701}{65519}e^{3} - \frac{5183578}{65519}e^{2} - \frac{28299089}{196557}e + \frac{10404115}{65519}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $-1$ |