Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 2x^{7} + 14x^{6} + 2x^{5} + 93x^{4} - 6x^{3} + 411x^{2} - 319x + 841\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1132}{336719}e^{7} + \frac{82}{19807}e^{6} + \frac{12397}{336719}e^{5} - \frac{5479}{336719}e^{4} + \frac{121980}{336719}e^{3} + \frac{12493}{336719}e^{2} + \frac{33207}{19807}e - \frac{16889}{11611}$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{223389}{13805479}e^{7} - \frac{35254}{812087}e^{6} - \frac{3844761}{13805479}e^{5} - \frac{1804384}{13805479}e^{4} - \frac{17846409}{13805479}e^{3} + \frac{8874505}{13805479}e^{2} - \frac{4376945}{812087}e + \frac{1679325}{476051}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{49549}{13805479}e^{7} - \frac{14643}{812087}e^{6} - \frac{1034772}{13805479}e^{5} - \frac{4378908}{13805479}e^{4} - \frac{5276361}{13805479}e^{3} - \frac{12841911}{13805479}e^{2} - \frac{2232009}{812087}e - \frac{1415490}{476051}$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{82734}{13805479}e^{7} - \frac{19851}{812087}e^{6} - \frac{1402804}{13805479}e^{5} - \frac{3076807}{13805479}e^{4} - \frac{7152977}{13805479}e^{3} - \frac{17409327}{13805479}e^{2} - \frac{927008}{812087}e - \frac{1918930}{476051}$ |
| 11 | $[11, 11, w + 9]$ | $\phantom{-}\frac{118404}{13805479}e^{7} + \frac{28174}{812087}e^{6} + \frac{1720267}{13805479}e^{5} + \frac{2391943}{13805479}e^{4} + \frac{6362292}{13805479}e^{3} + \frac{13339380}{13805479}e^{2} + \frac{1237337}{812087}e - \frac{67479}{476051}$ |
| 17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{235945}{13805479}e^{7} + \frac{33084}{812087}e^{6} + \frac{2337936}{13805479}e^{5} + \frac{4038774}{13805479}e^{4} + \frac{11921268}{13805479}e^{3} + \frac{29014668}{13805479}e^{2} + \frac{386543}{812087}e + \frac{3198120}{476051}$ |
| 17 | $[17, 17, w + 14]$ | $-\frac{470383}{13805479}e^{7} - \frac{104588}{812087}e^{6} - \frac{7661581}{13805479}e^{5} - \frac{8392113}{13805479}e^{4} - \frac{27670803}{13805479}e^{3} - \frac{20260020}{13805479}e^{2} - \frac{5752910}{812087}e + \frac{904340}{476051}$ |
| 19 | $[19, 19, w]$ | $\phantom{-}\frac{177207}{13805479}e^{7} + \frac{9862}{812087}e^{6} + \frac{2862480}{13805479}e^{5} - \frac{1307750}{13805479}e^{4} + \frac{20066043}{13805479}e^{3} - \frac{10841114}{13805479}e^{2} + \frac{5537729}{812087}e - \frac{2901753}{476051}$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{28295}{13805479}e^{7} + \frac{26751}{812087}e^{6} + \frac{1890404}{13805479}e^{5} + \frac{8636131}{13805479}e^{4} + \frac{9639277}{13805479}e^{3} + \frac{23460627}{13805479}e^{2} + \frac{2624141}{812087}e + \frac{2585930}{476051}$ |
| 37 | $[37, 37, -w - 4]$ | $-\frac{15390}{476051}e^{7} - \frac{1542}{28003}e^{6} - \frac{136971}{476051}e^{5} + \frac{295488}{476051}e^{4} - \frac{471625}{476051}e^{3} + \frac{1755999}{476051}e^{2} - \frac{133893}{28003}e + \frac{10630862}{476051}$ |
| 37 | $[37, 37, w - 5]$ | $\phantom{-}\frac{4320}{476051}e^{7} - \frac{1041}{28003}e^{6} + \frac{38448}{476051}e^{5} - \frac{82944}{476051}e^{4} + \frac{717010}{476051}e^{3} - \frac{492912}{476051}e^{2} + \frac{37584}{28003}e + \frac{106054}{476051}$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{206998}{13805479}e^{7} + \frac{51669}{812087}e^{6} + \frac{3651276}{13805479}e^{5} + \frac{8688595}{13805479}e^{4} + \frac{18618063}{13805479}e^{3} + \frac{45313713}{13805479}e^{2} + \frac{2943405}{812087}e + \frac{4994670}{476051}$ |
| 43 | $[43, 43, w + 26]$ | $-\frac{267596}{13805479}e^{7} - \frac{73276}{812087}e^{6} - \frac{4095388}{13805479}e^{5} - \frac{6858642}{13805479}e^{4} - \frac{11244828}{13805479}e^{3} - \frac{32591659}{13805479}e^{2} - \frac{1700818}{812087}e - \frac{679994}{476051}$ |
| 49 | $[49, 7, -7]$ | $-\frac{120}{11611}e^{7} - \frac{28}{683}e^{6} - \frac{1068}{11611}e^{5} + \frac{2304}{11611}e^{4} + \frac{2660}{11611}e^{3} + \frac{13692}{11611}e^{2} - \frac{1044}{683}e + \frac{66075}{11611}$ |
| 53 | $[53, 53, -w - 10]$ | $-\frac{7250}{476051}e^{7} - \frac{781}{28003}e^{6} - \frac{64525}{476051}e^{5} + \frac{139200}{476051}e^{4} + \frac{63950}{476051}e^{3} + \frac{827225}{476051}e^{2} - \frac{63075}{28003}e + \frac{5492753}{476051}$ |
| 53 | $[53, 53, w - 11]$ | $\phantom{-}\frac{3560}{476051}e^{7} - \frac{80}{28003}e^{6} + \frac{31684}{476051}e^{5} - \frac{68352}{476051}e^{4} + \frac{17845}{476051}e^{3} - \frac{406196}{476051}e^{2} + \frac{30972}{28003}e + \frac{3322780}{476051}$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}\frac{712169}{13805479}e^{7} + \frac{178444}{812087}e^{6} + \frac{11527260}{13805479}e^{5} + \frac{15746307}{13805479}e^{4} + \frac{35334885}{13805479}e^{3} + \frac{55796600}{13805479}e^{2} + \frac{6417094}{812087}e + \frac{373112}{476051}$ |
| 61 | $[61, 61, w + 45]$ | $-\frac{463545}{13805479}e^{7} - \frac{88695}{812087}e^{6} - \frac{6267780}{13805479}e^{5} - \frac{12998282}{13805479}e^{4} - \frac{31959765}{13805479}e^{3} - \frac{77785515}{13805479}e^{2} - \frac{4466888}{812087}e - \frac{8573850}{476051}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |