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:
| \(x^{16} + 25x^{14} + 255x^{12} + 1368x^{10} + 4151x^{8} + 7153x^{6} + 6708x^{4} + 3064x^{2} + 507\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-e$ |
| 3 | $[3, 3, -2w - 21]$ | $-\frac{3}{22}e^{14} - \frac{28}{11}e^{12} - \frac{381}{22}e^{10} - \frac{1119}{22}e^{8} - \frac{582}{11}e^{6} + \frac{367}{22}e^{4} + \frac{1121}{22}e^{2} + \frac{355}{22}$ |
| 3 | $[3, 3, 2w - 23]$ | $-\frac{3}{22}e^{14} - \frac{28}{11}e^{12} - \frac{381}{22}e^{10} - \frac{1119}{22}e^{8} - \frac{582}{11}e^{6} + \frac{367}{22}e^{4} + \frac{1121}{22}e^{2} + \frac{355}{22}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{25}{572}e^{15} + \frac{215}{286}e^{13} + \frac{2449}{572}e^{11} + \frac{4001}{572}e^{9} - \frac{1964}{143}e^{7} - \frac{27823}{572}e^{5} - \frac{1567}{44}e^{3} - \frac{2687}{572}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{25}{572}e^{15} - \frac{215}{286}e^{13} - \frac{2449}{572}e^{11} - \frac{4001}{572}e^{9} + \frac{1964}{143}e^{7} + \frac{27823}{572}e^{5} + \frac{1567}{44}e^{3} + \frac{2687}{572}e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{51}{286}e^{15} + \frac{553}{143}e^{13} + \frac{9469}{286}e^{11} + \frac{40869}{286}e^{9} + \frac{47019}{143}e^{7} + \frac{111615}{286}e^{5} + \frac{4535}{22}e^{3} + \frac{9013}{286}e$ |
| 19 | $[19, 19, w + 16]$ | $-\frac{51}{286}e^{15} - \frac{553}{143}e^{13} - \frac{9469}{286}e^{11} - \frac{40869}{286}e^{9} - \frac{47019}{143}e^{7} - \frac{111615}{286}e^{5} - \frac{4535}{22}e^{3} - \frac{9013}{286}e$ |
| 31 | $[31, 31, w + 13]$ | $-\frac{111}{286}e^{15} - \frac{1212}{143}e^{13} - \frac{20895}{286}e^{11} - \frac{90683}{286}e^{9} - \frac{104716}{143}e^{7} - \frac{250817}{286}e^{5} - \frac{10837}{22}e^{3} - \frac{29105}{286}e$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{111}{286}e^{15} + \frac{1212}{143}e^{13} + \frac{20895}{286}e^{11} + \frac{90683}{286}e^{9} + \frac{104716}{143}e^{7} + \frac{250817}{286}e^{5} + \frac{10837}{22}e^{3} + \frac{29105}{286}e$ |
| 37 | $[37, 37, w + 18]$ | $\phantom{-}0$ |
| 49 | $[49, 7, -7]$ | $-\frac{7}{44}e^{14} - \frac{91}{22}e^{12} - \frac{1879}{44}e^{10} - \frac{9739}{44}e^{8} - \frac{6586}{11}e^{6} - \frac{35143}{44}e^{4} - \frac{20147}{44}e^{2} - \frac{3359}{44}$ |
| 53 | $[53, 53, -234w + 2683]$ | $-\frac{19}{44}e^{14} - \frac{203}{22}e^{12} - \frac{3403}{44}e^{10} - \frac{14259}{44}e^{8} - \frac{7904}{11}e^{6} - \frac{36359}{44}e^{4} - \frac{19535}{44}e^{2} - \frac{3699}{44}$ |
| 53 | $[53, 53, -234w - 2449]$ | $-\frac{19}{44}e^{14} - \frac{203}{22}e^{12} - \frac{3403}{44}e^{10} - \frac{14259}{44}e^{8} - \frac{7904}{11}e^{6} - \frac{36359}{44}e^{4} - \frac{19535}{44}e^{2} - \frac{3699}{44}$ |
| 59 | $[59, 59, w + 1]$ | $\phantom{-}\frac{72}{143}e^{15} + \frac{1553}{143}e^{13} + \frac{13225}{143}e^{11} + \frac{56974}{143}e^{9} + \frac{132667}{143}e^{7} + \frac{165927}{143}e^{5} + \frac{7855}{11}e^{3} + \frac{23281}{143}e$ |
| 59 | $[59, 59, w + 57]$ | $-\frac{72}{143}e^{15} - \frac{1553}{143}e^{13} - \frac{13225}{143}e^{11} - \frac{56974}{143}e^{9} - \frac{132667}{143}e^{7} - \frac{165927}{143}e^{5} - \frac{7855}{11}e^{3} - \frac{23281}{143}e$ |
| 89 | $[89, 89, w + 41]$ | $\phantom{-}\frac{2}{13}e^{15} + \frac{50}{13}e^{13} + \frac{510}{13}e^{11} + \frac{2723}{13}e^{9} + \frac{8081}{13}e^{7} + \frac{12967}{13}e^{5} + 765e^{3} + \frac{2566}{13}e$ |
| 89 | $[89, 89, w + 47]$ | $-\frac{2}{13}e^{15} - \frac{50}{13}e^{13} - \frac{510}{13}e^{11} - \frac{2723}{13}e^{9} - \frac{8081}{13}e^{7} - \frac{12967}{13}e^{5} - 765e^{3} - \frac{2566}{13}e$ |
| 97 | $[97, 97, w + 26]$ | $-\frac{13}{44}e^{15} - \frac{147}{22}e^{13} - \frac{2641}{44}e^{11} - \frac{11977}{44}e^{9} - \frac{7168}{11}e^{7} - \frac{34409}{44}e^{5} - \frac{17949}{44}e^{3} - \frac{3045}{44}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).