Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19,19,-w^{2} + 5]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 6x^{9} - 8x^{8} + 92x^{7} - 37x^{6} - 382x^{5} + 193x^{4} + 660x^{3} - 144x^{2} - 432x - 81\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $\phantom{-}\frac{179}{24246}e^{9} - \frac{157}{4041}e^{8} - \frac{815}{12123}e^{7} + \frac{14521}{24246}e^{6} - \frac{4651}{12123}e^{5} - \frac{27505}{12123}e^{4} + \frac{92771}{24246}e^{3} + \frac{6989}{4041}e^{2} - \frac{2745}{449}e + \frac{269}{898}$ |
4 | $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 3]$ | $\phantom{-}\frac{3071}{48492}e^{9} - \frac{7597}{16164}e^{8} + \frac{4205}{48492}e^{7} + \frac{295393}{48492}e^{6} - \frac{247861}{24246}e^{5} - \frac{185213}{12123}e^{4} + \frac{1631231}{48492}e^{3} + \frac{217661}{16164}e^{2} - \frac{51303}{1796}e - \frac{13967}{1796}$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ | $-\frac{2711}{48492}e^{9} + \frac{5621}{16164}e^{8} + \frac{14731}{48492}e^{7} - \frac{230941}{48492}e^{6} + \frac{85837}{24246}e^{5} + \frac{171521}{12123}e^{4} - \frac{542027}{48492}e^{3} - \frac{206365}{16164}e^{2} + \frac{13723}{1796}e - \frac{1957}{1796}$ |
11 | $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ | $\phantom{-}\frac{925}{16164}e^{9} - \frac{5653}{16164}e^{8} - \frac{5225}{16164}e^{7} + \frac{77527}{16164}e^{6} - \frac{9259}{2694}e^{5} - \frac{19784}{1347}e^{4} + \frac{169829}{16164}e^{3} + \frac{276701}{16164}e^{2} - \frac{28285}{5388}e - \frac{11171}{1796}$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{2273}{48492}e^{9} + \frac{4055}{16164}e^{8} + \frac{18373}{48492}e^{7} - \frac{154051}{48492}e^{6} + \frac{18379}{24246}e^{5} + \frac{80957}{12123}e^{4} + \frac{94495}{48492}e^{3} + \frac{21761}{16164}e^{2} - \frac{54241}{5388}e - \frac{18727}{1796}$ |
19 | $[19, 19, -w^{2} + 5]$ | $-1$ |
31 | $[31, 31, w]$ | $-\frac{3433}{24246}e^{9} + \frac{2443}{2694}e^{8} + \frac{11237}{24246}e^{7} - \frac{284801}{24246}e^{6} + \frac{159854}{12123}e^{5} + \frac{343244}{12123}e^{4} - \frac{978589}{24246}e^{3} - \frac{36941}{2694}e^{2} + \frac{64477}{2694}e - \frac{3935}{898}$ |
31 | $[31, 31, w + 3]$ | $\phantom{-}\frac{164}{12123}e^{9} - \frac{980}{4041}e^{8} + \frac{9704}{12123}e^{7} + \frac{31816}{12123}e^{6} - \frac{163277}{12123}e^{5} - \frac{20849}{12123}e^{4} + \frac{552737}{12123}e^{3} - \frac{11936}{4041}e^{2} - \frac{60938}{1347}e - \frac{3333}{449}$ |
31 | $[31, 31, -w + 4]$ | $\phantom{-}\frac{163}{12123}e^{9} - \frac{34}{449}e^{8} - \frac{1394}{12123}e^{7} + \frac{14111}{12123}e^{6} - \frac{10555}{12123}e^{5} - \frac{48475}{12123}e^{4} + \frac{100906}{12123}e^{3} + \frac{145}{1347}e^{2} - \frac{19691}{1347}e + \frac{408}{449}$ |
31 | $[31, 31, w - 1]$ | $-\frac{637}{16164}e^{9} + \frac{181}{1796}e^{8} + \frac{17141}{16164}e^{7} - \frac{41411}{16164}e^{6} - \frac{68257}{8082}e^{5} + \frac{74620}{4041}e^{4} + \frac{309647}{16164}e^{3} - \frac{166651}{5388}e^{2} - \frac{80651}{5388}e + \frac{6359}{1796}$ |
41 | $[41, 41, -w^{2} + 2]$ | $\phantom{-}\frac{295}{4041}e^{9} - \frac{821}{1347}e^{8} + \frac{2047}{4041}e^{7} + \frac{30290}{4041}e^{6} - \frac{71272}{4041}e^{5} - \frac{58948}{4041}e^{4} + \frac{238873}{4041}e^{3} + \frac{5864}{1347}e^{2} - \frac{74878}{1347}e - \frac{3002}{449}$ |
41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ | $-\frac{623}{48492}e^{9} + \frac{309}{1796}e^{8} - \frac{24149}{48492}e^{7} - \frac{73717}{48492}e^{6} + \frac{193525}{24246}e^{5} - \frac{34780}{12123}e^{4} - \frac{880979}{48492}e^{3} + \frac{18115}{1796}e^{2} + \frac{57185}{5388}e - \frac{2361}{1796}$ |
59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ | $\phantom{-}\frac{1055}{8082}e^{9} - \frac{5399}{8082}e^{8} - \frac{11857}{8082}e^{7} + \frac{80297}{8082}e^{6} + \frac{2269}{1347}e^{5} - \frac{49250}{1347}e^{4} + \frac{4447}{8082}e^{3} + \frac{335335}{8082}e^{2} + \frac{8077}{2694}e - \frac{1931}{898}$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ | $-\frac{677}{24246}e^{9} - \frac{335}{8082}e^{8} + \frac{31201}{24246}e^{7} - \frac{8761}{24246}e^{6} - \frac{169838}{12123}e^{5} + \frac{108580}{12123}e^{4} + \frac{1048609}{24246}e^{3} - \frac{100157}{8082}e^{2} - \frac{118525}{2694}e - \frac{7785}{898}$ |
79 | $[79, 79, -w^{2} + 8]$ | $-\frac{487}{48492}e^{9} - \frac{293}{5388}e^{8} + \frac{30419}{48492}e^{7} + \frac{28099}{48492}e^{6} - \frac{188749}{24246}e^{5} - \frac{6068}{12123}e^{4} + \frac{1289261}{48492}e^{3} + \frac{1995}{1796}e^{2} - \frac{110527}{5388}e - \frac{11849}{1796}$ |
79 | $[79, 79, w^{2} - 2w - 7]$ | $-\frac{332}{4041}e^{9} + \frac{2294}{4041}e^{8} + \frac{856}{4041}e^{7} - \frac{32978}{4041}e^{6} + \frac{13297}{1347}e^{5} + \frac{37979}{1347}e^{4} - \frac{173449}{4041}e^{3} - \frac{140479}{4041}e^{2} + \frac{20158}{449}e + \frac{11010}{449}$ |
81 | $[81, 3, -3]$ | $-\frac{1295}{24246}e^{9} + \frac{2219}{8082}e^{8} + \frac{18091}{24246}e^{7} - \frac{117877}{24246}e^{6} - \frac{21368}{12123}e^{5} + \frac{303400}{12123}e^{4} - \frac{132515}{24246}e^{3} - \frac{325849}{8082}e^{2} + \frac{11085}{898}e + \frac{10661}{898}$ |
101 | $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ | $-\frac{103}{12123}e^{9} + \frac{92}{1347}e^{8} + \frac{509}{12123}e^{7} - \frac{18635}{12123}e^{6} + \frac{24346}{12123}e^{5} + \frac{117922}{12123}e^{4} - \frac{207181}{12123}e^{3} - \frac{14534}{1347}e^{2} + \frac{23351}{1347}e - \frac{1715}{449}$ |
101 | $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ | $\phantom{-}\frac{5897}{48492}e^{9} - \frac{11255}{16164}e^{8} - \frac{47581}{48492}e^{7} + \frac{485335}{48492}e^{6} - \frac{95701}{24246}e^{5} - \frac{409076}{12123}e^{4} + \frac{897689}{48492}e^{3} + \frac{512695}{16164}e^{2} - \frac{53363}{5388}e + \frac{10367}{1796}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,-w^{2} + 5]$ | $1$ |