Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[15, 15, -w + 4]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 8x^{8} - 11x^{7} + 196x^{6} - 142x^{5} - 1360x^{4} + 1801x^{3} + 2166x^{2} - 3168x - 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 7 | $[7, 7, w - 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{334039}{30758536}e^{8} + \frac{257509}{3844817}e^{7} + \frac{7237781}{30758536}e^{6} - \frac{12998311}{7689634}e^{5} - \frac{19820119}{15379268}e^{4} + \frac{45955793}{3844817}e^{3} + \frac{13938577}{30758536}e^{2} - \frac{277483881}{15379268}e - \frac{395225}{3844817}$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}\frac{60983}{15379268}e^{8} - \frac{102034}{3844817}e^{7} - \frac{1389257}{15379268}e^{6} + \frac{5281101}{7689634}e^{5} + \frac{5202935}{7689634}e^{4} - \frac{38650879}{7689634}e^{3} - \frac{36819091}{15379268}e^{2} + \frac{34768066}{3844817}e + \frac{16609574}{3844817}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{107885}{15379268}e^{8} - \frac{290971}{7689634}e^{7} - \frac{2901083}{15379268}e^{6} + \frac{3956093}{3844817}e^{5} + \frac{11822993}{7689634}e^{4} - \frac{62283853}{7689634}e^{3} - \frac{51890641}{15379268}e^{2} + \frac{130852057}{7689634}e + \frac{8609634}{3844817}$ |
| 13 | $[13, 13, -w + 2]$ | $-\frac{65493}{15379268}e^{8} + \frac{150123}{7689634}e^{7} + \frac{1762851}{15379268}e^{6} - \frac{3656041}{7689634}e^{5} - \frac{6715005}{7689634}e^{4} + \frac{10974085}{3844817}e^{3} + \frac{14312135}{15379268}e^{2} - \frac{7734255}{3844817}e + \frac{10915190}{3844817}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{269727}{15379268}e^{8} - \frac{835949}{7689634}e^{7} - \frac{6005835}{15379268}e^{6} + \frac{10697504}{3844817}e^{5} + \frac{9337900}{3844817}e^{4} - \frac{79167045}{3844817}e^{3} - \frac{42835545}{15379268}e^{2} + \frac{285679515}{7689634}e - \frac{1152496}{3844817}$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}\frac{38265}{3844817}e^{8} - \frac{445419}{7689634}e^{7} - \frac{842400}{3844817}e^{6} + \frac{5442111}{3844817}e^{5} + \frac{10830837}{7689634}e^{4} - \frac{38471426}{3844817}e^{3} - \frac{21070089}{7689634}e^{2} + \frac{132674669}{7689634}e + \frac{18051580}{3844817}$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{129413}{15379268}e^{8} + \frac{459725}{7689634}e^{7} + \frac{2232577}{15379268}e^{6} - \frac{5439852}{3844817}e^{5} - \frac{3337475}{7689634}e^{4} + \frac{71281027}{7689634}e^{3} - \frac{23861237}{15379268}e^{2} - \frac{54164873}{3844817}e + \frac{752094}{3844817}$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $\phantom{-}\frac{24329}{7689634}e^{8} - \frac{236401}{7689634}e^{7} - \frac{30695}{7689634}e^{6} + \frac{2759610}{3844817}e^{5} - \frac{7531093}{7689634}e^{4} - \frac{18927932}{3844817}e^{3} + \frac{25782504}{3844817}e^{2} + \frac{68666519}{7689634}e - \frac{9277916}{3844817}$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $-\frac{584937}{30758536}e^{8} + \frac{1005107}{7689634}e^{7} + \frac{11980555}{30758536}e^{6} - \frac{26107697}{7689634}e^{5} - \frac{27553985}{15379268}e^{4} + \frac{192410209}{7689634}e^{3} - \frac{56302701}{30758536}e^{2} - \frac{643178419}{15379268}e - \frac{3360060}{3844817}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{242597}{30758536}e^{8} - \frac{384151}{7689634}e^{7} - \frac{5275939}{30758536}e^{6} + \frac{9421653}{7689634}e^{5} + \frac{17721375}{15379268}e^{4} - \frac{32368850}{3844817}e^{3} - \frac{70213683}{30758536}e^{2} + \frac{202180319}{15379268}e - \frac{8307788}{3844817}$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{570885}{30758536}e^{8} + \frac{527523}{3844817}e^{7} + \frac{9609379}{30758536}e^{6} - \frac{13198616}{3844817}e^{5} - \frac{7207743}{15379268}e^{4} + \frac{93762857}{3844817}e^{3} - \frac{221073821}{30758536}e^{2} - \frac{613574029}{15379268}e + \frac{23931644}{3844817}$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $\phantom{-}\frac{275993}{15379268}e^{8} - \frac{465751}{3844817}e^{7} - \frac{4928993}{15379268}e^{6} + \frac{22658083}{7689634}e^{5} + \frac{6036719}{7689634}e^{4} - \frac{155854271}{7689634}e^{3} + \frac{97872977}{15379268}e^{2} + \frac{246652121}{7689634}e - \frac{22265602}{3844817}$ |
| 43 | $[43, 43, -2w - 3]$ | $-\frac{460301}{30758536}e^{8} + \frac{753069}{7689634}e^{7} + \frac{8639863}{30758536}e^{6} - \frac{9272749}{3844817}e^{5} - \frac{10967385}{15379268}e^{4} + \frac{64315607}{3844817}e^{3} - \frac{222549173}{30758536}e^{2} - \frac{413694809}{15379268}e + \frac{34786314}{3844817}$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $-\frac{83057}{15379268}e^{8} + \frac{349241}{7689634}e^{7} + \frac{1233155}{15379268}e^{6} - \frac{8853241}{7689634}e^{5} + \frac{1241055}{7689634}e^{4} + \frac{30081470}{3844817}e^{3} - \frac{72699145}{15379268}e^{2} - \frac{33731861}{3844817}e + \frac{28094440}{3844817}$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}\frac{1146371}{30758536}e^{8} - \frac{1760753}{7689634}e^{7} - \frac{26085781}{30758536}e^{6} + \frac{22491744}{3844817}e^{5} + \frac{84192911}{15379268}e^{4} - \frac{163205599}{3844817}e^{3} - \frac{216658313}{30758536}e^{2} + \frac{1156623865}{15379268}e - \frac{1131380}{3844817}$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $-\frac{52542}{3844817}e^{8} + \frac{683049}{7689634}e^{7} + \frac{1100941}{3844817}e^{6} - \frac{8120094}{3844817}e^{5} - \frac{14206043}{7689634}e^{4} + \frac{52353095}{3844817}e^{3} + \frac{27703771}{7689634}e^{2} - \frac{147992973}{7689634}e - \frac{7773728}{3844817}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{1067461}{30758536}e^{8} - \frac{1725439}{7689634}e^{7} - \frac{21970255}{30758536}e^{6} + \frac{42669905}{7689634}e^{5} + \frac{56816005}{15379268}e^{4} - \frac{296757493}{7689634}e^{3} + \frac{8483625}{30758536}e^{2} + \frac{957127711}{15379268}e - \frac{11723414}{3844817}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 2]$ | $-1$ |
| $5$ | $[5, 5, w + 1]$ | $1$ |