Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w^{3} - 2w^{2} - 4w]$ |
| Dimension: | $9$ |
| 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:
| \(x^{9} + 3x^{8} - 10x^{7} - 35x^{6} + 13x^{5} + 104x^{4} + 54x^{3} - 35x^{2} - 15x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $-\frac{55}{89}e^{8} - \frac{62}{89}e^{7} + \frac{692}{89}e^{6} + \frac{676}{89}e^{5} - \frac{2269}{89}e^{4} - \frac{1953}{89}e^{3} + \frac{1414}{89}e^{2} + \frac{455}{89}e - \frac{19}{89}$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}\frac{111}{89}e^{8} + \frac{185}{89}e^{7} - \frac{1327}{89}e^{6} - \frac{2086}{89}e^{5} + \frac{3809}{89}e^{4} + \frac{6050}{89}e^{3} - \frac{619}{89}e^{2} - \frac{1517}{89}e - \frac{206}{89}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{111}{89}e^{8} + \frac{96}{89}e^{7} - \frac{1416}{89}e^{6} - \frac{1018}{89}e^{5} + \frac{4788}{89}e^{4} + \frac{2935}{89}e^{3} - \frac{3645}{89}e^{2} - \frac{360}{89}e + \frac{506}{89}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{56}{89}e^{8} + \frac{212}{89}e^{7} - \frac{546}{89}e^{6} - \frac{2478}{89}e^{5} + \frac{650}{89}e^{4} + \frac{7212}{89}e^{3} + \frac{3109}{89}e^{2} - \frac{2308}{89}e - \frac{492}{89}$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-\frac{57}{89}e^{8} - \frac{95}{89}e^{7} + \frac{667}{89}e^{6} + \frac{1076}{89}e^{5} - \frac{1790}{89}e^{4} - \frac{3126}{89}e^{3} - \frac{67}{89}e^{2} + \frac{512}{89}e - \frac{65}{89}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}\frac{33}{89}e^{8} - \frac{34}{89}e^{7} - \frac{433}{89}e^{6} + \frac{431}{89}e^{5} + \frac{1486}{89}e^{4} - \frac{1071}{89}e^{3} - \frac{1329}{89}e^{2} + \frac{261}{89}e - \frac{131}{89}$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $-\frac{121}{89}e^{8} - \frac{172}{89}e^{7} + \frac{1469}{89}e^{6} + \frac{1950}{89}e^{5} - \frac{4440}{89}e^{4} - \frac{6041}{89}e^{3} + \frac{1847}{89}e^{2} + \frac{2781}{89}e - \frac{113}{89}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}\frac{141}{89}e^{8} + \frac{146}{89}e^{7} - \frac{1753}{89}e^{6} - \frac{1589}{89}e^{5} + \frac{5613}{89}e^{4} + \frac{4777}{89}e^{3} - \frac{3502}{89}e^{2} - \frac{1571}{89}e + \frac{484}{89}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $-\frac{66}{89}e^{8} - \frac{110}{89}e^{7} + \frac{688}{89}e^{6} + \frac{1185}{89}e^{5} - \frac{1103}{89}e^{4} - \frac{3109}{89}e^{3} - \frac{2682}{89}e^{2} - \frac{433}{89}e + \frac{618}{89}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{36}{89}e^{8} + \frac{60}{89}e^{7} - \frac{440}{89}e^{6} - \frac{703}{89}e^{5} + \frac{1346}{89}e^{4} + \frac{2246}{89}e^{3} - \frac{576}{89}e^{2} - \frac{1204}{89}e - \frac{62}{89}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{77}{89}e^{8} - \frac{20}{89}e^{7} - \frac{1040}{89}e^{6} + \frac{353}{89}e^{5} + \frac{3942}{89}e^{4} - \frac{1075}{89}e^{3} - \frac{4525}{89}e^{2} + \frac{609}{89}e + \frac{436}{89}$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $-\frac{261}{89}e^{8} - \frac{435}{89}e^{7} + \frac{3101}{89}e^{6} + \frac{4941}{89}e^{5} - \frac{8824}{89}e^{4} - \frac{14637}{89}e^{3} + \frac{1595}{89}e^{2} + \frac{4368}{89}e - \frac{129}{89}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $-\frac{347}{89}e^{8} - \frac{430}{89}e^{7} + \frac{4251}{89}e^{6} + \frac{4697}{89}e^{5} - \frac{13147}{89}e^{4} - \frac{13545}{89}e^{3} + \frac{6442}{89}e^{2} + \frac{3081}{89}e - \frac{594}{89}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{56}{89}e^{8} + \frac{123}{89}e^{7} - \frac{635}{89}e^{6} - \frac{1410}{89}e^{5} + \frac{1629}{89}e^{4} + \frac{4186}{89}e^{3} + \frac{172}{89}e^{2} - \frac{1329}{89}e - \frac{225}{89}$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $-\frac{127}{89}e^{8} - \frac{93}{89}e^{7} + \frac{1661}{89}e^{6} + \frac{925}{89}e^{5} - \frac{6029}{89}e^{4} - \frac{2529}{89}e^{3} + \frac{5948}{89}e^{2} + \frac{460}{89}e - \frac{1052}{89}$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $-\frac{134}{89}e^{8} - \frac{253}{89}e^{7} + \frac{1529}{89}e^{6} + \frac{2948}{89}e^{5} - \frac{3774}{89}e^{4} - \frac{9260}{89}e^{3} - \frac{1505}{89}e^{2} + \frac{4175}{89}e + \frac{656}{89}$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $-\frac{301}{89}e^{8} - \frac{383}{89}e^{7} + \frac{3669}{89}e^{6} + \frac{4219}{89}e^{5} - \frac{11259}{89}e^{4} - \frac{12465}{89}e^{3} + \frac{5706}{89}e^{2} + \frac{3817}{89}e - \frac{1138}{89}$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{32}{89}e^{8} - \frac{83}{89}e^{7} + \frac{401}{89}e^{6} + \frac{1060}{89}e^{5} - \frac{1325}{89}e^{4} - \frac{3816}{89}e^{3} + \frac{779}{89}e^{2} + \frac{2959}{89}e - \frac{202}{89}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $-1$ |