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:
| \(x^{16} - 26x^{14} + 275x^{12} - 1529x^{10} + 4819x^{8} - 8614x^{6} + 8090x^{4} - 3076x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{12}{341}e^{15} - \frac{976}{1023}e^{13} + \frac{10795}{1023}e^{11} - \frac{20919}{341}e^{9} + \frac{68568}{341}e^{7} - \frac{125904}{341}e^{5} + \frac{358667}{1023}e^{3} - \frac{137527}{1023}e$ |
| 3 | $[3, 3, -2w - 21]$ | $\phantom{-}\frac{395}{1023}e^{14} - \frac{9307}{1023}e^{12} + \frac{85927}{1023}e^{10} - \frac{131462}{341}e^{8} + \frac{942134}{1023}e^{6} - \frac{1109440}{1023}e^{4} + \frac{504412}{1023}e^{2} - \frac{734}{341}$ |
| 3 | $[3, 3, 2w - 23]$ | $-\frac{398}{1023}e^{14} + \frac{9502}{1023}e^{12} - \frac{89242}{1023}e^{10} + \frac{139599}{341}e^{8} - \frac{1028840}{1023}e^{6} + \frac{1251400}{1023}e^{4} - \frac{587980}{1023}e^{2} + \frac{1040}{341}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{214}{1023}e^{15} - \frac{5044}{1023}e^{13} + \frac{15511}{341}e^{11} - \frac{212615}{1023}e^{9} + \frac{499535}{1023}e^{7} - \frac{184870}{341}e^{5} + \frac{190100}{1023}e^{3} + \frac{46705}{1023}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{470}{1023}e^{15} + \frac{11113}{1023}e^{13} - \frac{102989}{1023}e^{11} + \frac{474065}{1023}e^{9} - \frac{1130279}{1023}e^{7} + \frac{1304705}{1023}e^{5} - \frac{537382}{1023}e^{3} - \frac{38615}{1023}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{10}{33}e^{15} + \frac{232}{33}e^{13} - \frac{695}{11}e^{11} + \frac{9089}{33}e^{9} - \frac{19388}{33}e^{7} + \frac{5486}{11}e^{5} + \frac{1951}{33}e^{3} - \frac{6862}{33}e$ |
| 19 | $[19, 19, w + 2]$ | $-\frac{166}{341}e^{15} + \frac{11569}{1023}e^{13} - \frac{34754}{341}e^{11} + \frac{152468}{341}e^{9} - \frac{992237}{1023}e^{7} + \frac{299242}{341}e^{5} - \frac{5251}{341}e^{3} - \frac{276931}{1023}e$ |
| 19 | $[19, 19, w + 16]$ | $-\frac{164}{1023}e^{15} + \frac{4181}{1023}e^{13} - \frac{14258}{341}e^{11} + \frac{224854}{1023}e^{9} - \frac{645541}{1023}e^{7} + \frac{330657}{341}e^{5} - \frac{737590}{1023}e^{3} + \frac{200224}{1023}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{164}{1023}e^{15} - \frac{1280}{341}e^{13} + \frac{11871}{341}e^{11} - \frac{169612}{1023}e^{9} + \frac{152891}{341}e^{7} - \frac{250181}{341}e^{5} + \frac{734521}{1023}e^{3} - \frac{109821}{341}e$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{37}{1023}e^{15} + \frac{359}{1023}e^{13} + \frac{1262}{341}e^{11} - \frac{69598}{1023}e^{9} + \frac{385673}{1023}e^{7} - \frac{328107}{341}e^{5} + \frac{1170142}{1023}e^{3} - \frac{511772}{1023}e$ |
| 37 | $[37, 37, w + 18]$ | $\phantom{-}\frac{668}{1023}e^{15} - \frac{5380}{341}e^{13} + \frac{51563}{341}e^{11} - \frac{752563}{1023}e^{9} + \frac{659654}{341}e^{7} - \frac{923001}{341}e^{5} + \frac{1850386}{1023}e^{3} - \frac{140087}{341}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{1394}{1023}e^{14} + \frac{32981}{1023}e^{12} - \frac{102097}{341}e^{10} + \frac{1417150}{1023}e^{8} - \frac{3419104}{1023}e^{6} + \frac{1354685}{341}e^{4} - \frac{1854247}{1023}e^{2} + \frac{3724}{1023}$ |
| 53 | $[53, 53, -234w + 2683]$ | $-\frac{283}{1023}e^{14} + \frac{2267}{341}e^{12} - \frac{21489}{341}e^{10} + \frac{306557}{1023}e^{8} - \frac{255877}{341}e^{6} + \frac{319794}{341}e^{4} - \frac{468203}{1023}e^{2} + \frac{2268}{341}$ |
| 53 | $[53, 53, -234w - 2449]$ | $\phantom{-}\frac{917}{1023}e^{14} - \frac{21754}{1023}e^{12} + \frac{67576}{341}e^{10} - \frac{942391}{1023}e^{8} + \frac{2289065}{1023}e^{6} - \frac{916103}{341}e^{4} + \frac{1271572}{1023}e^{2} - \frac{1664}{1023}$ |
| 59 | $[59, 59, w + 1]$ | $-\frac{197}{341}e^{15} + \frac{14545}{1023}e^{13} - \frac{142919}{1023}e^{11} + \frac{239671}{341}e^{9} - \frac{1976146}{1023}e^{7} + \frac{975042}{341}e^{5} - \frac{2105773}{1023}e^{3} + \frac{179291}{341}e$ |
| 59 | $[59, 59, w + 57]$ | $\phantom{-}\frac{74}{1023}e^{15} - \frac{1741}{1023}e^{13} + \frac{5319}{341}e^{11} - \frac{71542}{1023}e^{9} + \frac{159584}{1023}e^{7} - \frac{50679}{341}e^{5} + \frac{17731}{1023}e^{3} + \frac{37372}{1023}e$ |
| 89 | $[89, 89, w + 41]$ | $-\frac{79}{341}e^{15} + \frac{2066}{341}e^{13} - \frac{21823}{341}e^{11} + \frac{119388}{341}e^{9} - \frac{360018}{341}e^{7} + \frac{587440}{341}e^{5} - \frac{472095}{341}e^{3} + \frac{143183}{341}e$ |
| 89 | $[89, 89, w + 47]$ | $\phantom{-}\frac{655}{341}e^{15} - \frac{46567}{1023}e^{13} + \frac{432907}{1023}e^{11} - \frac{2001044}{1023}e^{9} + \frac{4794704}{1023}e^{7} - \frac{5550718}{1023}e^{5} + \frac{744878}{341}e^{3} + \frac{85328}{341}e$ |
| 97 | $[97, 97, w + 26]$ | $-\frac{268}{341}e^{15} + \frac{6508}{341}e^{13} - \frac{62896}{341}e^{11} + \frac{310331}{341}e^{9} - \frac{836394}{341}e^{7} + \frac{1224501}{341}e^{5} - \frac{896725}{341}e^{3} + \frac{252508}{341}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).