Base field \(\Q(\sqrt{145}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 36\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 4, w]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 80x^{12} + 1422x^{8} + 3856x^{4} + 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{25}{10752}e^{13} - \frac{1997}{10752}e^{9} - \frac{11637}{3584}e^{5} - \frac{80107}{10752}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{13}{13824}e^{15} + \frac{7415}{96768}e^{11} + \frac{15461}{10752}e^{7} + \frac{468913}{96768}e^{3}$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{29}{5376}e^{14} + \frac{2305}{5376}e^{10} + \frac{13417}{1792}e^{6} + \frac{102551}{5376}e^{2}$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{53}{4608}e^{15} + \frac{4249}{4608}e^{11} + \frac{8459}{512}e^{7} + \frac{218687}{4608}e^{3}$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{3}{512}e^{13} - \frac{1657}{3584}e^{9} - \frac{28291}{3584}e^{5} - \frac{58719}{3584}e$ |
| 29 | $[29, 29, w + 14]$ | $-\frac{53}{5376}e^{14} - \frac{607}{768}e^{10} - \frac{25377}{1792}e^{6} - \frac{212543}{5376}e^{2}$ |
| 37 | $[37, 37, w + 10]$ | $\phantom{-}\frac{53}{10752}e^{13} + \frac{607}{1536}e^{9} + \frac{25377}{3584}e^{5} + \frac{191039}{10752}e$ |
| 37 | $[37, 37, w + 26]$ | $-\frac{3743}{96768}e^{15} - \frac{42781}{13824}e^{11} - \frac{591649}{10752}e^{7} - \frac{14489789}{96768}e^{3}$ |
| 43 | $[43, 43, w + 19]$ | $\phantom{-}\frac{5}{1536}e^{13} + \frac{2911}{10752}e^{9} + \frac{18903}{3584}e^{5} + \frac{225545}{10752}e$ |
| 43 | $[43, 43, w + 23]$ | $\phantom{-}\frac{5353}{96768}e^{15} + \frac{427997}{96768}e^{11} + \frac{843863}{10752}e^{7} + \frac{20413531}{96768}e^{3}$ |
| 47 | $[47, 47, w + 22]$ | $-\frac{101}{10752}e^{15} - \frac{8137}{10752}e^{11} - \frac{49297}{3584}e^{7} - \frac{454031}{10752}e^{3}$ |
| 47 | $[47, 47, w + 24]$ | $-\frac{15}{3584}e^{13} - \frac{1147}{3584}e^{9} - \frac{2495}{512}e^{5} - \frac{16781}{3584}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{1}{448}e^{12} - \frac{85}{448}e^{8} - \frac{1655}{448}e^{4} - \frac{2659}{448}$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{3}{256}e^{14} - \frac{1657}{1792}e^{10} - \frac{28291}{1792}e^{6} - \frac{62303}{1792}e^{2}$ |
| 59 | $[59, 59, w + 42]$ | $\phantom{-}\frac{53}{2688}e^{14} + \frac{607}{384}e^{10} + \frac{25377}{896}e^{6} + \frac{217919}{2688}e^{2}$ |
| 71 | $[71, 71, w + 21]$ | $\phantom{-}\frac{9}{448}e^{14} + \frac{717}{448}e^{10} + \frac{12527}{448}e^{6} + \frac{4221}{64}e^{2}$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{37}{1792}e^{14} + \frac{2953}{1792}e^{10} + \frac{52211}{1792}e^{6} + \frac{142799}{1792}e^{2}$ |
| 73 | $[73, 73, w + 13]$ | $\phantom{-}\frac{917}{13824}e^{15} + \frac{513871}{96768}e^{11} + \frac{1016749}{10752}e^{7} + \frac{24923033}{96768}e^{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{53}{32256}e^{14} + \frac{607}{4608}e^{10} + \frac{8459}{3584}e^{6} + \frac{223295}{32256}e^{2}$ |