Base field \(\Q(\sqrt{481}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 120\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 28x^{14} + 309x^{12} + 1687x^{10} + 4653x^{8} + 5832x^{6} + 2520x^{4} + 214x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{136}{881}e^{15} - \frac{49558}{11453}e^{13} - \frac{547429}{11453}e^{11} - \frac{2989973}{11453}e^{9} - \frac{8236688}{11453}e^{7} - \frac{10252158}{11453}e^{5} - \frac{4277047}{11453}e^{3} - \frac{254021}{11453}e$ |
| 3 | $[3, 3, -2w - 21]$ | $\phantom{-}\frac{539}{11453}e^{14} + \frac{14657}{11453}e^{12} + \frac{156623}{11453}e^{10} + \frac{824724}{11453}e^{8} + \frac{2178564}{11453}e^{6} + \frac{2568576}{11453}e^{4} + \frac{74916}{881}e^{2} + \frac{42326}{11453}$ |
| 3 | $[3, 3, 2w - 23]$ | $-\frac{340}{11453}e^{14} - \frac{9056}{11453}e^{12} - \frac{94940}{11453}e^{10} - \frac{491537}{11453}e^{8} - \frac{1279288}{11453}e^{6} - \frac{1488442}{11453}e^{4} - \frac{569086}{11453}e^{2} - \frac{31874}{11453}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{3954}{11453}e^{15} + \frac{111058}{11453}e^{13} + \frac{1228421}{11453}e^{11} + \frac{6710163}{11453}e^{9} + \frac{18442691}{11453}e^{7} + \frac{22782508}{11453}e^{5} + \frac{9326630}{11453}e^{3} + \frac{45349}{881}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{1502}{11453}e^{15} + \frac{42359}{11453}e^{13} + \frac{470043}{11453}e^{11} + \frac{2572463}{11453}e^{9} + \frac{7069345}{11453}e^{7} + \frac{8703327}{11453}e^{5} + \frac{3546522}{11453}e^{3} + \frac{246611}{11453}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{136}{881}e^{15} - \frac{49558}{11453}e^{13} - \frac{547429}{11453}e^{11} - \frac{2989973}{11453}e^{9} - \frac{8236688}{11453}e^{7} - \frac{10252158}{11453}e^{5} - \frac{4277047}{11453}e^{3} - \frac{242568}{11453}e$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{396}{881}e^{15} + \frac{143783}{11453}e^{13} + \frac{1581780}{11453}e^{11} + \frac{8600922}{11453}e^{9} + \frac{23589905}{11453}e^{7} + \frac{29300314}{11453}e^{5} + \frac{12427765}{11453}e^{3} + \frac{1046937}{11453}e$ |
| 19 | $[19, 19, w + 16]$ | $\phantom{-}\frac{3270}{11453}e^{15} + \frac{91917}{11453}e^{13} + \frac{1017472}{11453}e^{11} + \frac{5562436}{11453}e^{9} + \frac{15306033}{11453}e^{7} + \frac{18955485}{11453}e^{5} + \frac{600932}{881}e^{3} + \frac{454820}{11453}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{4656}{11453}e^{15} + \frac{129984}{11453}e^{13} + \frac{110051}{881}e^{11} + \frac{7796678}{11453}e^{9} + \frac{21508645}{11453}e^{7} + \frac{27082511}{11453}e^{5} + \frac{11805215}{11453}e^{3} + \frac{883713}{11453}e$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{1309}{11453}e^{15} - \frac{37861}{11453}e^{13} - \frac{431594}{11453}e^{11} - \frac{2432074}{11453}e^{9} - \frac{531767}{881}e^{7} - \frac{8922629}{11453}e^{5} - \frac{4059494}{11453}e^{3} - \frac{488418}{11453}e$ |
| 37 | $[37, 37, w + 18]$ | $-\frac{10186}{11453}e^{15} - \frac{285258}{11453}e^{13} - \frac{3146681}{11453}e^{11} - \frac{1319487}{881}e^{9} - \frac{47132626}{11453}e^{7} - \frac{58507957}{11453}e^{5} - \frac{24516928}{11453}e^{3} - \frac{1744325}{11453}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{790}{11453}e^{14} - \frac{24825}{11453}e^{12} - \frac{301907}{11453}e^{10} - \frac{1779556}{11453}e^{8} - \frac{5153612}{11453}e^{6} - \frac{6434975}{11453}e^{4} - \frac{2376275}{11453}e^{2} - \frac{4210}{881}$ |
| 53 | $[53, 53, -234w + 2683]$ | $-\frac{627}{11453}e^{14} - \frac{19675}{11453}e^{12} - \frac{239549}{11453}e^{10} - \frac{1420855}{11453}e^{8} - \frac{322275}{881}e^{6} - \frac{5496448}{11453}e^{4} - \frac{2345511}{11453}e^{2} - \frac{83038}{11453}$ |
| 53 | $[53, 53, -234w - 2449]$ | $-\frac{1201}{11453}e^{14} - \frac{32984}{11453}e^{12} - \frac{355210}{11453}e^{10} - \frac{144651}{881}e^{8} - \frac{4979639}{11453}e^{6} - \frac{5839831}{11453}e^{4} - \frac{2075702}{11453}e^{2} - \frac{72598}{11453}$ |
| 59 | $[59, 59, w + 1]$ | $-\frac{485}{881}e^{15} - \frac{176901}{11453}e^{13} - \frac{1957197}{11453}e^{11} - \frac{10720289}{11453}e^{9} - \frac{29700904}{11453}e^{7} - \frac{37493582}{11453}e^{5} - \frac{16410889}{11453}e^{3} - \frac{1266569}{11453}e$ |
| 59 | $[59, 59, w + 57]$ | $-\frac{5580}{11453}e^{15} - \frac{154481}{11453}e^{13} - \frac{129659}{881}e^{11} - \frac{9105274}{11453}e^{9} - \frac{24910434}{11453}e^{7} - \frac{31201347}{11453}e^{5} - \frac{13822389}{11453}e^{3} - \frac{1377264}{11453}e$ |
| 89 | $[89, 89, w + 41]$ | $\phantom{-}\frac{11823}{11453}e^{15} + \frac{332612}{11453}e^{13} + \frac{3688417}{11453}e^{11} + \frac{20234042}{11453}e^{9} + \frac{56061844}{11453}e^{7} + \frac{70538384}{11453}e^{5} + \frac{30561691}{11453}e^{3} + \frac{2545951}{11453}e$ |
| 89 | $[89, 89, w + 47]$ | $-\frac{2559}{11453}e^{15} - \frac{71777}{11453}e^{13} - \frac{794475}{11453}e^{11} - \frac{335474}{881}e^{9} - \frac{12154734}{11453}e^{7} - \frac{15539624}{11453}e^{5} - \frac{6844758}{11453}e^{3} - \frac{369442}{11453}e$ |
| 97 | $[97, 97, w + 26]$ | $-\frac{4688}{11453}e^{15} - \frac{132930}{11453}e^{13} - \frac{1487328}{11453}e^{11} - \frac{8246117}{11453}e^{9} - \frac{23165212}{11453}e^{7} - \frac{29799307}{11453}e^{5} - \frac{13580789}{11453}e^{3} - \frac{1311386}{11453}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).