Base field \(\Q(\sqrt{3}, \sqrt{11})\)
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[11,11,-w^{2} - w + 1]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} + 6x^{11} + 2x^{10} - 47x^{9} - 67x^{8} + 102x^{7} + 214x^{6} - 57x^{5} - 231x^{4} - 21x^{3} + 80x^{2} + 10x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{2}w^{3} + \frac{7}{2}w - 1]$ | $\phantom{-}e$ |
2 | $[2, 2, -w + 1]$ | $\phantom{-}\frac{1}{14}e^{11} + \frac{2}{7}e^{10} - \frac{5}{7}e^{9} - \frac{53}{14}e^{8} + \frac{3}{2}e^{7} + \frac{124}{7}e^{6} + \frac{24}{7}e^{5} - \frac{495}{14}e^{4} - \frac{155}{14}e^{3} + \frac{411}{14}e^{2} + \frac{39}{7}e - \frac{45}{7}$ |
9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w]$ | $\phantom{-}\frac{1}{14}e^{11} + \frac{4}{7}e^{10} + \frac{8}{7}e^{9} - \frac{5}{2}e^{8} - \frac{167}{14}e^{7} - \frac{41}{7}e^{6} + \frac{195}{7}e^{5} + \frac{419}{14}e^{4} - \frac{277}{14}e^{3} - \frac{409}{14}e^{2} + \frac{4}{7}e + \frac{34}{7}$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $-\frac{8}{7}e^{11} - \frac{46}{7}e^{10} - \frac{4}{7}e^{9} + \frac{375}{7}e^{8} + 60e^{7} - \frac{927}{7}e^{6} - \frac{1329}{7}e^{5} + \frac{901}{7}e^{4} + \frac{1303}{7}e^{3} - \frac{369}{7}e^{2} - \frac{316}{7}e + \frac{62}{7}$ |
11 | $[11, 11, w^{2} + w - 1]$ | $\phantom{-}1$ |
25 | $[25, 5, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ | $-\frac{17}{14}e^{11} - \frac{40}{7}e^{10} + \frac{32}{7}e^{9} + \frac{99}{2}e^{8} + \frac{277}{14}e^{7} - \frac{934}{7}e^{6} - \frac{606}{7}e^{5} + \frac{1851}{14}e^{4} + \frac{1181}{14}e^{3} - \frac{509}{14}e^{2} - \frac{110}{7}e + \frac{38}{7}$ |
25 | $[25, 5, -\frac{1}{2}w^{3} - w^{2} + \frac{7}{2}w + 4]$ | $\phantom{-}\frac{33}{14}e^{11} + 12e^{10} - \frac{41}{7}e^{9} - \frac{1461}{14}e^{8} - \frac{929}{14}e^{7} + \frac{2026}{7}e^{6} + 252e^{5} - \frac{4567}{14}e^{4} - \frac{3665}{14}e^{3} + \frac{2067}{14}e^{2} + \frac{468}{7}e - \frac{186}{7}$ |
37 | $[37, 37, -w^{3} + 7w + 1]$ | $\phantom{-}\frac{31}{14}e^{11} + 11e^{10} - \frac{47}{7}e^{9} - \frac{1347}{14}e^{8} - \frac{703}{14}e^{7} + \frac{1889}{7}e^{6} + 197e^{5} - \frac{4325}{14}e^{4} - \frac{2801}{14}e^{3} + \frac{1929}{14}e^{2} + \frac{348}{7}e - \frac{148}{7}$ |
37 | $[37, 37, -2w + 1]$ | $-\frac{9}{14}e^{11} - \frac{25}{7}e^{10} + \frac{3}{7}e^{9} + \frac{435}{14}e^{8} + \frac{61}{2}e^{7} - \frac{605}{7}e^{6} - \frac{797}{7}e^{5} + \frac{1389}{14}e^{4} + \frac{1899}{14}e^{3} - \frac{717}{14}e^{2} - \frac{302}{7}e + \frac{90}{7}$ |
37 | $[37, 37, 2w + 1]$ | $-\frac{11}{14}e^{11} - \frac{31}{7}e^{10} + \frac{509}{14}e^{8} + \frac{545}{14}e^{7} - \frac{611}{7}e^{6} - \frac{883}{7}e^{5} + \frac{919}{14}e^{4} + \frac{229}{2}e^{3} - \frac{47}{14}e^{2} - \frac{100}{7}e - \frac{4}{7}$ |
37 | $[37, 37, -w^{3} + 7w - 1]$ | $\phantom{-}\frac{9}{14}e^{11} + \frac{27}{7}e^{10} + \frac{10}{7}e^{9} - \frac{417}{14}e^{8} - \frac{629}{14}e^{7} + \frac{412}{7}e^{6} + \frac{989}{7}e^{5} - \frac{111}{14}e^{4} - \frac{1867}{14}e^{3} - \frac{649}{14}e^{2} + \frac{148}{7}e + \frac{66}{7}$ |
49 | $[49, 7, \frac{1}{2}w^{3} - \frac{9}{2}w + 2]$ | $-\frac{9}{7}e^{11} - \frac{47}{7}e^{10} + \frac{22}{7}e^{9} + \frac{431}{7}e^{8} + \frac{300}{7}e^{7} - \frac{1293}{7}e^{6} - \frac{1278}{7}e^{5} + \frac{1574}{7}e^{4} + \frac{1545}{7}e^{3} - \frac{751}{7}e^{2} - \frac{464}{7}e + \frac{120}{7}$ |
49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{9}{2}w + 2]$ | $\phantom{-}2e^{11} + \frac{73}{7}e^{10} - \frac{26}{7}e^{9} - \frac{620}{7}e^{8} - \frac{456}{7}e^{7} + \frac{1646}{7}e^{6} + \frac{1597}{7}e^{5} - \frac{1733}{7}e^{4} - \frac{1551}{7}e^{3} + \frac{708}{7}e^{2} + 42e - \frac{130}{7}$ |
83 | $[83, 83, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 2]$ | $-\frac{11}{7}e^{11} - \frac{66}{7}e^{10} - \frac{19}{7}e^{9} + \frac{526}{7}e^{8} + \frac{705}{7}e^{7} - \frac{1214}{7}e^{6} - \frac{2213}{7}e^{5} + \frac{943}{7}e^{4} + \frac{2180}{7}e^{3} - \frac{193}{7}e^{2} - \frac{438}{7}e + \frac{58}{7}$ |
83 | $[83, 83, w^{2} + w - 5]$ | $-\frac{26}{7}e^{11} - \frac{131}{7}e^{10} + \frac{74}{7}e^{9} + 165e^{8} + \frac{653}{7}e^{7} - \frac{3286}{7}e^{6} - \frac{2573}{7}e^{5} + \frac{3848}{7}e^{4} + \frac{2680}{7}e^{3} - \frac{1798}{7}e^{2} - \frac{656}{7}e + \frac{276}{7}$ |
83 | $[83, 83, w^{2} - w - 5]$ | $\phantom{-}\frac{13}{7}e^{11} + \frac{60}{7}e^{10} - \frac{64}{7}e^{9} - \frac{569}{7}e^{8} - \frac{131}{7}e^{7} + \frac{1787}{7}e^{6} + \frac{916}{7}e^{5} - \frac{2262}{7}e^{4} - \frac{1125}{7}e^{3} + 149e^{2} + \frac{300}{7}e - 18$ |
83 | $[83, 83, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 2]$ | $\phantom{-}2e^{11} + \frac{73}{7}e^{10} - \frac{26}{7}e^{9} - \frac{627}{7}e^{8} - \frac{484}{7}e^{7} + \frac{1674}{7}e^{6} + \frac{1800}{7}e^{5} - \frac{1670}{7}e^{4} - \frac{1922}{7}e^{3} + \frac{512}{7}e^{2} + 68e - \frac{88}{7}$ |
97 | $[97, 97, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 8]$ | $\phantom{-}\frac{3}{2}e^{11} + \frac{50}{7}e^{10} - \frac{53}{7}e^{9} - \frac{999}{14}e^{8} - \frac{227}{14}e^{7} + \frac{1734}{7}e^{6} + \frac{880}{7}e^{5} - \frac{5255}{14}e^{4} - \frac{2637}{14}e^{3} + \frac{3307}{14}e^{2} + 74e - \frac{314}{7}$ |
97 | $[97, 97, \frac{5}{2}w^{3} - w^{2} - \frac{31}{2}w + 6]$ | $\phantom{-}\frac{25}{14}e^{11} + \frac{72}{7}e^{10} + \frac{4}{7}e^{9} - \frac{171}{2}e^{8} - \frac{1305}{14}e^{7} + \frac{1523}{7}e^{6} + \frac{2117}{7}e^{5} - \frac{2951}{14}e^{4} - \frac{4153}{14}e^{3} + \frac{961}{14}e^{2} + \frac{464}{7}e - \frac{60}{7}$ |
97 | $[97, 97, -\frac{11}{2}w^{3} + 4w^{2} + \frac{71}{2}w - 26]$ | $-\frac{67}{14}e^{11} - 24e^{10} + \frac{93}{7}e^{9} + \frac{2923}{14}e^{8} + \frac{1677}{14}e^{7} - \frac{4068}{7}e^{6} - 461e^{5} + \frac{9255}{14}e^{4} + \frac{6691}{14}e^{3} - \frac{4063}{14}e^{2} - \frac{856}{7}e + \frac{272}{7}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,-w^{2} - w + 1]$ | $-1$ |