Base field 4.4.13768.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w + 3]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} - 5x^{14} - 11x^{13} + 87x^{12} + 3x^{11} - 580x^{10} + 406x^{9} + 1830x^{8} - 2012x^{7} - 2671x^{6} + 3809x^{5} + 1359x^{4} - 2752x^{3} + 62x^{2} + 508x - 66\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{69}{400}e^{14} + \frac{89}{200}e^{13} + \frac{1213}{400}e^{12} - \frac{761}{100}e^{11} - \frac{8299}{400}e^{10} + \frac{19963}{400}e^{9} + \frac{5519}{80}e^{8} - \frac{12497}{80}e^{7} - \frac{44827}{400}e^{6} + \frac{46769}{200}e^{5} + \frac{30513}{400}e^{4} - \frac{3557}{25}e^{3} - \frac{358}{25}e^{2} + \frac{4109}{200}e + \frac{161}{200}$ |
| 4 | $[4, 2, -w^{2} - w + 1]$ | $\phantom{-}\frac{1027}{400}e^{14} - \frac{1587}{200}e^{13} - \frac{17379}{400}e^{12} + \frac{14063}{100}e^{11} + \frac{110717}{400}e^{10} - \frac{385429}{400}e^{9} - \frac{63897}{80}e^{8} + \frac{254911}{80}e^{7} + \frac{366141}{400}e^{6} - \frac{1025427}{200}e^{5} - \frac{1279}{400}e^{4} + \frac{86781}{25}e^{3} - \frac{10611}{25}e^{2} - \frac{125347}{200}e + \frac{18137}{200}$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-\frac{1887}{400}e^{14} + \frac{2947}{200}e^{13} + \frac{31799}{400}e^{12} - \frac{26103}{100}e^{11} - \frac{201377}{400}e^{10} + \frac{715249}{400}e^{9} + \frac{115037}{80}e^{8} - \frac{473171}{80}e^{7} - \frac{641121}{400}e^{6} + \frac{1906187}{200}e^{5} - \frac{37101}{400}e^{4} - \frac{162061}{25}e^{3} + \frac{20741}{25}e^{2} + \frac{237407}{200}e - \frac{33997}{200}$ |
| 17 | $[17, 17, -w + 3]$ | $-1$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 3w + 5]$ | $\phantom{-}\frac{759}{80}e^{14} - \frac{1199}{40}e^{13} - \frac{12743}{80}e^{12} + \frac{10631}{20}e^{11} + \frac{80249}{80}e^{10} - \frac{291713}{80}e^{9} - \frac{45413}{16}e^{8} + \frac{193347}{16}e^{7} + \frac{247497}{80}e^{6} - \frac{780799}{40}e^{5} + \frac{23677}{80}e^{4} + \frac{66572}{5}e^{3} - \frac{8332}{5}e^{2} - \frac{97639}{40}e + \frac{13789}{40}$ |
| 31 | $[31, 31, -w^{2} - 2w + 1]$ | $\phantom{-}\frac{751}{200}e^{14} - \frac{1181}{100}e^{13} - \frac{12627}{200}e^{12} + \frac{10469}{50}e^{11} + \frac{79721}{200}e^{10} - \frac{287277}{200}e^{9} - \frac{45341}{40}e^{8} + \frac{190503}{40}e^{7} + \frac{250833}{200}e^{6} - \frac{770301}{100}e^{5} + \frac{15273}{200}e^{4} + \frac{131656}{25}e^{3} - \frac{15836}{25}e^{2} - \frac{96611}{100}e + \frac{13081}{100}$ |
| 41 | $[41, 41, -w^{2} + 5]$ | $-\frac{1427}{400}e^{14} + \frac{2187}{200}e^{13} + \frac{24179}{400}e^{12} - \frac{19363}{100}e^{11} - \frac{154317}{400}e^{10} + \frac{530229}{400}e^{9} + \frac{89337}{80}e^{8} - \frac{350511}{80}e^{7} - \frac{516541}{400}e^{6} + \frac{1411427}{200}e^{5} + \frac{13679}{400}e^{4} - \frac{120156}{25}e^{3} + \frac{14111}{25}e^{2} + \frac{177747}{200}e - \frac{22737}{200}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $-\frac{457}{400}e^{14} + \frac{617}{200}e^{13} + \frac{8089}{400}e^{12} - \frac{5433}{100}e^{11} - \frac{55047}{400}e^{10} + \frac{147439}{400}e^{9} + \frac{35467}{80}e^{8} - \frac{96061}{80}e^{7} - \frac{261431}{400}e^{6} + \frac{377657}{200}e^{5} + \frac{124989}{400}e^{4} - \frac{30796}{25}e^{3} + \frac{1101}{25}e^{2} + \frac{42177}{200}e - \frac{4067}{200}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $-\frac{1959}{200}e^{14} + \frac{3079}{100}e^{13} + \frac{32943}{200}e^{12} - \frac{27271}{50}e^{11} - \frac{208089}{200}e^{10} + \frac{747393}{200}e^{9} + \frac{118509}{40}e^{8} - \frac{494707}{40}e^{7} - \frac{658497}{200}e^{6} + \frac{1995059}{100}e^{5} - \frac{34957}{200}e^{4} - \frac{339729}{25}e^{3} + \frac{41549}{25}e^{2} + \frac{248199}{100}e - \frac{34829}{100}$ |
| 59 | $[59, 59, -w - 3]$ | $\phantom{-}\frac{1079}{200}e^{14} - \frac{1649}{100}e^{13} - \frac{18283}{200}e^{12} + \frac{14551}{50}e^{11} + \frac{117009}{200}e^{10} - \frac{396933}{200}e^{9} - \frac{68389}{40}e^{8} + \frac{261247}{40}e^{7} + \frac{408857}{200}e^{6} - \frac{1046729}{100}e^{5} - \frac{39183}{200}e^{4} + \frac{177199}{25}e^{3} - \frac{20294}{25}e^{2} - \frac{130019}{100}e + \frac{18849}{100}$ |
| 59 | $[59, 59, -2w^{3} + 2w^{2} + 9w - 5]$ | $-\frac{262}{25}e^{14} + \frac{819}{25}e^{13} + \frac{4424}{25}e^{12} - \frac{14537}{25}e^{11} - \frac{28102}{25}e^{10} + \frac{99799}{25}e^{9} + \frac{16157}{5}e^{8} - \frac{66176}{5}e^{7} - \frac{92196}{25}e^{6} + \frac{534424}{25}e^{5} + \frac{749}{25}e^{4} - \frac{364051}{25}e^{3} + \frac{41306}{25}e^{2} + \frac{66314}{25}e - \frac{8844}{25}$ |
| 59 | $[59, 59, -w^{3} - 3w^{2} - w + 3]$ | $-\frac{881}{200}e^{14} + \frac{1361}{100}e^{13} + \frac{14937}{200}e^{12} - \frac{12089}{50}e^{11} - \frac{95351}{200}e^{10} + \frac{332287}{200}e^{9} + \frac{55171}{40}e^{8} - \frac{220613}{40}e^{7} - \frac{318223}{200}e^{6} + \frac{892781}{100}e^{5} + \frac{6237}{200}e^{4} - \frac{152911}{25}e^{3} + \frac{17891}{25}e^{2} + \frac{114341}{100}e - \frac{15411}{100}$ |
| 59 | $[59, 59, w^{3} - 7w + 1]$ | $-\frac{1823}{400}e^{14} + \frac{2863}{200}e^{13} + \frac{30671}{400}e^{12} - \frac{25387}{100}e^{11} - \frac{193633}{400}e^{10} + \frac{696521}{400}e^{9} + \frac{109933}{80}e^{8} - \frac{461419}{80}e^{7} - \frac{603409}{400}e^{6} + \frac{1861023}{200}e^{5} - \frac{47029}{400}e^{4} - \frac{158169}{25}e^{3} + \frac{19489}{25}e^{2} + \frac{229703}{200}e - \frac{32613}{200}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 2w + 5]$ | $\phantom{-}\frac{3377}{400}e^{14} - \frac{5237}{200}e^{13} - \frac{57129}{400}e^{12} + \frac{46413}{100}e^{11} + \frac{363967}{400}e^{10} - \frac{1272479}{400}e^{9} - \frac{210227}{80}e^{8} + \frac{842301}{80}e^{7} + \frac{1208591}{400}e^{6} - \frac{3396077}{200}e^{5} - \frac{11229}{400}e^{4} + \frac{289331}{25}e^{3} - \frac{34961}{25}e^{2} - \frac{428297}{200}e + \frac{59987}{200}$ |
| 61 | $[61, 61, -w^{3} - w^{2} + 4w + 3]$ | $\phantom{-}\frac{3121}{400}e^{14} - \frac{4901}{200}e^{13} - \frac{52617}{400}e^{12} + \frac{43549}{100}e^{11} + \frac{332991}{400}e^{10} - \frac{1197567}{400}e^{9} - \frac{189651}{80}e^{8} + \frac{795373}{80}e^{7} + \frac{1046543}{400}e^{6} - \frac{3217821}{200}e^{5} + \frac{76883}{400}e^{4} + \frac{274838}{25}e^{3} - \frac{33878}{25}e^{2} - \frac{405481}{200}e + \frac{54851}{200}$ |
| 67 | $[67, 67, 4w^{3} - 4w^{2} - 18w + 7]$ | $\phantom{-}\frac{151}{200}e^{14} - \frac{231}{100}e^{13} - \frac{2527}{200}e^{12} + \frac{2019}{50}e^{11} + \frac{15921}{200}e^{10} - \frac{54577}{200}e^{9} - \frac{9101}{40}e^{8} + \frac{35643}{40}e^{7} + \frac{52233}{200}e^{6} - \frac{141951}{100}e^{5} - \frac{2827}{200}e^{4} + \frac{23881}{25}e^{3} - \frac{2536}{25}e^{2} - \frac{17311}{100}e + \frac{2581}{100}$ |
| 73 | $[73, 73, -2w^{3} + 6w - 3]$ | $\phantom{-}\frac{1687}{100}e^{14} - \frac{2647}{50}e^{13} - \frac{28399}{100}e^{12} + \frac{23453}{25}e^{11} + \frac{179677}{100}e^{10} - \frac{642949}{100}e^{9} - \frac{102657}{20}e^{8} + \frac{425651}{20}e^{7} + \frac{576421}{100}e^{6} - \frac{1716537}{50}e^{5} + \frac{15501}{100}e^{4} + \frac{584519}{25}e^{3} - \frac{69039}{25}e^{2} - \frac{214057}{50}e + \frac{28997}{50}$ |
| 73 | $[73, 73, -2w + 3]$ | $\phantom{-}\frac{4603}{400}e^{14} - \frac{7143}{200}e^{13} - \frac{77731}{400}e^{12} + \frac{63207}{100}e^{11} + \frac{494213}{400}e^{10} - \frac{1729781}{400}e^{9} - \frac{284833}{80}e^{8} + \frac{1142559}{80}e^{7} + \frac{1635349}{400}e^{6} - \frac{4594303}{200}e^{5} - \frac{25631}{400}e^{4} + \frac{389809}{25}e^{3} - \frac{45854}{25}e^{2} - \frac{570483}{200}e + \frac{78193}{200}$ |
| 97 | $[97, 97, w^{3} - 2w^{2} - 5w + 3]$ | $\phantom{-}\frac{899}{200}e^{14} - \frac{1369}{100}e^{13} - \frac{15223}{200}e^{12} + \frac{12081}{50}e^{11} + \frac{97029}{200}e^{10} - \frac{329273}{200}e^{9} - \frac{55969}{40}e^{8} + \frac{216187}{40}e^{7} + \frac{318517}{200}e^{6} - \frac{861749}{100}e^{5} + \frac{8277}{200}e^{4} + \frac{144544}{25}e^{3} - \frac{20164}{25}e^{2} - \frac{105739}{100}e + \frac{16469}{100}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w + 3]$ | $1$ |