Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{2} + 3]$ |
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:
\(x^{9} + 2x^{8} - 24x^{7} - 34x^{6} + 173x^{5} + 154x^{4} - 444x^{3} - 306x^{2} + 368x + 245\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $\phantom{-}\frac{49787}{798007}e^{8} + \frac{188199}{798007}e^{7} - \frac{130483}{114001}e^{6} - \frac{3378358}{798007}e^{5} + \frac{3830616}{798007}e^{4} + \frac{15002032}{798007}e^{3} - \frac{2900951}{798007}e^{2} - \frac{18763825}{798007}e - \frac{789127}{114001}$ |
5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{56307}{798007}e^{8} + \frac{167084}{798007}e^{7} - \frac{156881}{114001}e^{6} - \frac{2770342}{798007}e^{5} + \frac{5122178}{798007}e^{4} + \frac{10396889}{798007}e^{3} - \frac{4181843}{798007}e^{2} - \frac{11055246}{798007}e - \frac{875003}{114001}$ |
13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}1$ |
13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}\frac{18976}{798007}e^{8} + \frac{41357}{798007}e^{7} - \frac{61303}{114001}e^{6} - \frac{556872}{798007}e^{5} + \frac{3052054}{798007}e^{4} + \frac{645896}{798007}e^{3} - \frac{9302245}{798007}e^{2} + \frac{2397956}{798007}e + \frac{1243547}{114001}$ |
16 | $[16, 2, 2]$ | $-\frac{146439}{798007}e^{8} - \frac{416172}{798007}e^{7} + \frac{412420}{114001}e^{6} + \frac{6743584}{798007}e^{5} - \frac{13891106}{798007}e^{4} - \frac{24052818}{798007}e^{3} + \frac{13459300}{798007}e^{2} + \frac{24933215}{798007}e + \frac{1338415}{114001}$ |
19 | $[19, 19, -w^{2} + w + 1]$ | $\phantom{-}\frac{8027}{798007}e^{8} - \frac{53534}{798007}e^{7} - \frac{41137}{114001}e^{6} + \frac{1417309}{798007}e^{5} + \frac{2725656}{798007}e^{4} - \frac{10153691}{798007}e^{3} - \frac{7827353}{798007}e^{2} + \frac{16080101}{798007}e + \frac{1421259}{114001}$ |
23 | $[23, 23, -w^{3} + 4w + 2]$ | $-\frac{79661}{798007}e^{8} - \frac{347255}{798007}e^{7} + \frac{177790}{114001}e^{6} + \frac{6084539}{798007}e^{5} - \frac{2502229}{798007}e^{4} - \frac{25183838}{798007}e^{3} - \frac{8108710}{798007}e^{2} + \frac{28227487}{798007}e + \frac{2376046}{114001}$ |
25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{26433}{798007}e^{8} - \frac{8028}{798007}e^{7} + \frac{109574}{114001}e^{6} + \frac{64161}{798007}e^{5} - \frac{6450565}{798007}e^{4} - \frac{215083}{798007}e^{3} + \frac{15191504}{798007}e^{2} + \frac{793577}{798007}e - \frac{1281921}{114001}$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{1237}{114001}e^{8} + \frac{1152}{114001}e^{7} - \frac{30827}{114001}e^{6} - \frac{30678}{114001}e^{5} + \frac{180801}{114001}e^{4} + \frac{335037}{114001}e^{3} + \frac{11633}{114001}e^{2} - \frac{1129150}{114001}e - \frac{701469}{114001}$ |
29 | $[29, 29, -w + 3]$ | $-\frac{101777}{798007}e^{8} - \frac{361308}{798007}e^{7} + \frac{265794}{114001}e^{6} + \frac{6280053}{798007}e^{5} - \frac{7517728}{798007}e^{4} - \frac{26351091}{798007}e^{3} + \frac{3567980}{798007}e^{2} + \frac{32689486}{798007}e + \frac{1616572}{114001}$ |
31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{45506}{798007}e^{8} - \frac{318949}{798007}e^{7} + \frac{59262}{114001}e^{6} + \frac{5920937}{798007}e^{5} + \frac{3106994}{798007}e^{4} - \frac{26797826}{798007}e^{3} - \frac{18610416}{798007}e^{2} + \frac{32025986}{798007}e + \frac{3174251}{114001}$ |
37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{5818}{114001}e^{8} + \frac{2231}{114001}e^{7} + \frac{179088}{114001}e^{6} - \frac{88506}{114001}e^{5} - \frac{1658232}{114001}e^{4} + \frac{707922}{114001}e^{3} + \frac{4909629}{114001}e^{2} - \frac{1269792}{114001}e - \frac{3935088}{114001}$ |
37 | $[37, 37, w^{3} - 3w + 1]$ | $-\frac{83942}{798007}e^{8} - \frac{216505}{798007}e^{7} + \frac{249011}{114001}e^{6} + \frac{3541960}{798007}e^{5} - \frac{9439839}{798007}e^{4} - \frac{13388044}{798007}e^{3} + \frac{14200664}{798007}e^{2} + \frac{16561340}{798007}e - \frac{465082}{114001}$ |
53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}\frac{156874}{798007}e^{8} + \frac{193280}{798007}e^{7} - \frac{539820}{114001}e^{6} - \frac{2221061}{798007}e^{5} + \frac{25660349}{798007}e^{4} + \frac{883278}{798007}e^{3} - \frac{50438034}{798007}e^{2} + \frac{6192105}{798007}e + \frac{3690907}{114001}$ |
59 | $[59, 59, w^{2} + w - 4]$ | $\phantom{-}\frac{24205}{114001}e^{8} + \frac{117005}{114001}e^{7} - \frac{363409}{114001}e^{6} - \frac{2115390}{114001}e^{5} + \frac{560527}{114001}e^{4} + \frac{9308542}{114001}e^{3} + \frac{3165758}{114001}e^{2} - \frac{11025028}{114001}e - \frac{6920035}{114001}$ |
61 | $[61, 61, -2w^{2} + w + 8]$ | $-\frac{210519}{798007}e^{8} - \frac{580726}{798007}e^{7} + \frac{612417}{114001}e^{6} + \frac{9438239}{798007}e^{5} - \frac{22878781}{798007}e^{4} - \frac{33884313}{798007}e^{3} + \frac{35536150}{798007}e^{2} + \frac{34812926}{798007}e - \frac{525625}{114001}$ |
73 | $[73, 73, -w^{3} + 5w - 1]$ | $-\frac{345073}{798007}e^{8} - \frac{851185}{798007}e^{7} + \frac{1041586}{114001}e^{6} + \frac{13760312}{798007}e^{5} - \frac{40656415}{798007}e^{4} - \frac{50091819}{798007}e^{3} + \frac{59768939}{798007}e^{2} + \frac{54383043}{798007}e - \frac{712111}{114001}$ |
79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{28776}{798007}e^{8} + \frac{54025}{798007}e^{7} + \frac{136650}{114001}e^{6} - \frac{1409603}{798007}e^{5} - \frac{9291826}{798007}e^{4} + \frac{9325996}{798007}e^{3} + \frac{29155743}{798007}e^{2} - \frac{16212036}{798007}e - \frac{4323283}{114001}$ |
79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $\phantom{-}\frac{52180}{798007}e^{8} + \frac{166374}{798007}e^{7} - \frac{132933}{114001}e^{6} - \frac{2859498}{798007}e^{5} + \frac{2664820}{798007}e^{4} + \frac{12364137}{798007}e^{3} + \frac{10125040}{798007}e^{2} - \frac{19471888}{798007}e - \frac{3862514}{114001}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{2} + 3]$ | $-1$ |