Base field 3.3.1620.1
Generator \(w\), with minimal polynomial \(x^{3} - 12x - 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, -w - 3]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 20x^{9} - 2x^{8} + 146x^{7} + 21x^{6} - 470x^{5} - 47x^{4} + 637x^{3} - 37x^{2} - 270x + 81\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{12}e^{10} + \frac{1}{4}e^{9} - \frac{23}{12}e^{8} - \frac{53}{12}e^{7} + \frac{185}{12}e^{6} + 27e^{5} - \frac{313}{6}e^{4} - \frac{779}{12}e^{3} + \frac{211}{3}e^{2} + \frac{569}{12}e - \frac{111}{4}$ |
| 5 | $[5, 5, -w - 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -2w^{2} + 3w + 19]$ | $\phantom{-}\frac{1}{4}e^{10} - \frac{1}{4}e^{9} - \frac{17}{4}e^{8} + \frac{13}{4}e^{7} + \frac{101}{4}e^{6} - 13e^{5} - 61e^{4} + \frac{65}{4}e^{3} + \frac{103}{2}e^{2} - \frac{1}{4}e - \frac{39}{4}$ |
| 7 | $[7, 7, -w^{2} + 2w + 7]$ | $\phantom{-}\frac{2}{3}e^{10} + \frac{3}{4}e^{9} - \frac{83}{6}e^{8} - \frac{175}{12}e^{7} + \frac{617}{6}e^{6} + \frac{389}{4}e^{5} - \frac{3931}{12}e^{4} - \frac{3013}{12}e^{3} + \frac{1253}{3}e^{2} + \frac{583}{3}e - \frac{583}{4}$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $-\frac{1}{3}e^{10} - \frac{1}{4}e^{9} + \frac{20}{3}e^{8} + \frac{65}{12}e^{7} - \frac{289}{6}e^{6} - \frac{155}{4}e^{5} + \frac{1799}{12}e^{4} + \frac{1241}{12}e^{3} - \frac{559}{3}e^{2} - \frac{469}{6}e + \frac{257}{4}$ |
| 17 | $[17, 17, w^{2} - w - 3]$ | $-\frac{3}{4}e^{10} + \frac{57}{4}e^{8} + \frac{5}{2}e^{7} - \frac{389}{4}e^{6} - \frac{121}{4}e^{5} + \frac{1133}{4}e^{4} + 105e^{3} - \frac{643}{2}e^{2} - \frac{389}{4}e + 93$ |
| 23 | $[23, 23, -w + 3]$ | $\phantom{-}\frac{1}{2}e^{10} + \frac{1}{2}e^{9} - \frac{21}{2}e^{8} - \frac{21}{2}e^{7} + \frac{159}{2}e^{6} + 75e^{5} - 260e^{4} - \frac{413}{2}e^{3} + 344e^{2} + \frac{343}{2}e - \frac{255}{2}$ |
| 37 | $[37, 37, 3w + 5]$ | $-\frac{7}{12}e^{10} + \frac{1}{2}e^{9} + \frac{125}{12}e^{8} - \frac{41}{6}e^{7} - \frac{785}{12}e^{6} + \frac{119}{4}e^{5} + \frac{2015}{12}e^{4} - \frac{136}{3}e^{3} - \frac{451}{3}e^{2} + \frac{199}{12}e + 26$ |
| 43 | $[43, 43, w^{2} + 3w + 3]$ | $-2e^{10} + 38e^{8} + 7e^{7} - 259e^{6} - 85e^{5} + 752e^{4} + 296e^{3} - 853e^{2} - 276e + 260$ |
| 47 | $[47, 47, -w^{2} + 3]$ | $\phantom{-}\frac{3}{2}e^{10} - \frac{3}{4}e^{9} - \frac{55}{2}e^{8} + \frac{29}{4}e^{7} + 180e^{6} - \frac{31}{4}e^{5} - \frac{1987}{4}e^{4} - \frac{259}{4}e^{3} + 520e^{2} + 111e - \frac{549}{4}$ |
| 49 | $[49, 7, -w^{2} + 5]$ | $-\frac{1}{3}e^{10} - \frac{1}{4}e^{9} + \frac{20}{3}e^{8} + \frac{65}{12}e^{7} - \frac{289}{6}e^{6} - \frac{155}{4}e^{5} + \frac{1811}{12}e^{4} + \frac{1253}{12}e^{3} - \frac{577}{3}e^{2} - \frac{511}{6}e + \frac{269}{4}$ |
| 53 | $[53, 53, -w^{2} + w + 13]$ | $\phantom{-}\frac{1}{2}e^{10} - \frac{19}{2}e^{8} - 2e^{7} + \frac{131}{2}e^{6} + \frac{49}{2}e^{5} - \frac{393}{2}e^{4} - 88e^{3} + 240e^{2} + \frac{175}{2}e - 84$ |
| 61 | $[61, 61, -w^{2} + 15]$ | $\phantom{-}\frac{2}{3}e^{10} - \frac{1}{2}e^{9} - \frac{37}{3}e^{8} + \frac{37}{6}e^{7} + \frac{244}{3}e^{6} - \frac{41}{2}e^{5} - \frac{1349}{6}e^{4} + \frac{37}{6}e^{3} + \frac{698}{3}e^{2} + \frac{100}{3}e - \frac{119}{2}$ |
| 61 | $[61, 61, w^{2} - 2w - 13]$ | $-\frac{19}{12}e^{10} + \frac{365}{12}e^{8} + \frac{17}{3}e^{7} - \frac{2513}{12}e^{6} - \frac{275}{4}e^{5} + \frac{7349}{12}e^{4} + \frac{1429}{6}e^{3} - \frac{2080}{3}e^{2} - \frac{2645}{12}e + \frac{403}{2}$ |
| 61 | $[61, 61, -4w - 5]$ | $\phantom{-}\frac{7}{6}e^{10} - e^{9} - \frac{125}{6}e^{8} + \frac{38}{3}e^{7} + \frac{791}{6}e^{6} - \frac{95}{2}e^{5} - \frac{2075}{6}e^{4} + \frac{146}{3}e^{3} + \frac{983}{3}e^{2} + \frac{71}{6}e - 64$ |
| 67 | $[67, 67, -2w^{2} + 6w + 13]$ | $-\frac{1}{12}e^{10} - \frac{1}{4}e^{9} + \frac{29}{12}e^{8} + \frac{47}{12}e^{7} - \frac{269}{12}e^{6} - 21e^{5} + \frac{251}{3}e^{4} + \frac{539}{12}e^{3} - \frac{725}{6}e^{2} - \frac{395}{12}e + \frac{173}{4}$ |
| 73 | $[73, 73, 2w^{2} - 2w - 17]$ | $-\frac{1}{3}e^{10} + \frac{20}{3}e^{8} + \frac{2}{3}e^{7} - \frac{143}{3}e^{6} - 8e^{5} + \frac{437}{3}e^{4} + \frac{83}{3}e^{3} - \frac{535}{3}e^{2} - \frac{89}{3}e + 56$ |
| 79 | $[79, 79, -w - 5]$ | $\phantom{-}\frac{5}{12}e^{10} - \frac{1}{2}e^{9} - \frac{79}{12}e^{8} + \frac{37}{6}e^{7} + \frac{427}{12}e^{6} - \frac{89}{4}e^{5} - \frac{913}{12}e^{4} + \frac{65}{3}e^{3} + \frac{170}{3}e^{2} + \frac{19}{12}e - 16$ |
| 79 | $[79, 79, 2w^{2} - 4w - 17]$ | $-\frac{1}{3}e^{10} + \frac{1}{2}e^{9} + \frac{17}{3}e^{8} - \frac{47}{6}e^{7} - \frac{98}{3}e^{6} + \frac{83}{2}e^{5} + \frac{421}{6}e^{4} - \frac{491}{6}e^{3} - \frac{109}{3}e^{2} + \frac{115}{3}e - \frac{5}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w - 3]$ | $-1$ |