Properties

Label 6.6.1312625.1-41.2-c
Base field 6.6.1312625.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$
Dimension $11$
CM no
Base change no

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Base field 6.6.1312625.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 7x^{3} + 12x^{2} - 12x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$
Dimension: $11$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{11} - 10x^{10} + 24x^{9} + 58x^{8} - 299x^{7} + 99x^{6} + 944x^{5} - 892x^{4} - 904x^{3} + 979x^{2} + 183x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{3011}{11219}e^{10} - \frac{21910}{11219}e^{9} + \frac{14723}{11219}e^{8} + \frac{196659}{11219}e^{7} - \frac{339277}{11219}e^{6} - \frac{479955}{11219}e^{5} + \frac{1342}{13}e^{4} + \frac{181074}{11219}e^{3} - \frac{1039569}{11219}e^{2} + \frac{196107}{11219}e + \frac{55891}{11219}$
16 $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ $\phantom{-}\frac{1279}{11219}e^{10} - \frac{7496}{11219}e^{9} - \frac{6910}{11219}e^{8} + \frac{92851}{11219}e^{7} - \frac{26673}{11219}e^{6} - \frac{415719}{11219}e^{5} + \frac{231}{13}e^{4} + \frac{827635}{11219}e^{3} - \frac{245663}{11219}e^{2} - \frac{676483}{11219}e - \frac{51159}{11219}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 3]$ $...$
29 $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ $-\frac{35017}{11219}e^{10} + \frac{270262}{11219}e^{9} - \frac{226883}{11219}e^{8} - \frac{2525544}{11219}e^{7} + \frac{4693861}{11219}e^{6} + \frac{7026170}{11219}e^{5} - \frac{19334}{13}e^{4} - \frac{6197461}{11219}e^{3} + \frac{16278611}{11219}e^{2} + \frac{2222101}{11219}e - \frac{30476}{11219}$
31 $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ $-\frac{2015}{863}e^{10} + \frac{15381}{863}e^{9} - \frac{11999}{863}e^{8} - \frac{145135}{863}e^{7} + \frac{259807}{863}e^{6} + \frac{412693}{863}e^{5} - 1076e^{4} - \frac{387736}{863}e^{3} + \frac{904412}{863}e^{2} + \frac{153976}{863}e + \frac{3060}{863}$
41 $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ $...$
41 $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ $-1$
59 $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ $...$
61 $[61, 61, w^{5} - 7w^{3} + 10w]$ $...$
61 $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ $...$
71 $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ $-\frac{3994}{11219}e^{10} + \frac{29715}{11219}e^{9} - \frac{21061}{11219}e^{8} - \frac{275837}{11219}e^{7} + \frac{477002}{11219}e^{6} + \frac{754965}{11219}e^{5} - \frac{1943}{13}e^{4} - \frac{600464}{11219}e^{3} + \frac{1558878}{11219}e^{2} + \frac{44456}{11219}e + \frac{46909}{11219}$
71 $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ $-\frac{691}{863}e^{10} + \frac{5066}{863}e^{9} - \frac{2940}{863}e^{8} - \frac{48698}{863}e^{7} + \frac{76309}{863}e^{6} + \frac{143468}{863}e^{5} - 315e^{4} - \frac{145657}{863}e^{3} + \frac{249229}{863}e^{2} + \frac{61177}{863}e + \frac{10870}{863}$
71 $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ $...$
79 $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ $-\frac{29385}{11219}e^{10} + \frac{232175}{11219}e^{9} - \frac{212426}{11219}e^{8} - \frac{2182003}{11219}e^{7} + \frac{4185243}{11219}e^{6} + \frac{6213979}{11219}e^{5} - \frac{17222}{13}e^{4} - \frac{6126916}{11219}e^{3} + \frac{14554971}{11219}e^{2} + \frac{2989456}{11219}e + \frac{78836}{11219}$
79 $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ $-\frac{1963}{863}e^{10} + \frac{15307}{863}e^{9} - \frac{13510}{863}e^{8} - \frac{142698}{863}e^{7} + \frac{271036}{863}e^{6} + \frac{397945}{863}e^{5} - 1113e^{4} - \frac{365943}{863}e^{3} + \frac{935948}{863}e^{2} + \frac{157981}{863}e + \frac{7992}{863}$
79 $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ $...$
89 $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ $...$
89 $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ $...$
89 $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ $-\frac{1278}{863}e^{10} + \frac{9984}{863}e^{9} - \frac{8039}{863}e^{8} - \frac{97700}{863}e^{7} + \frac{173350}{863}e^{6} + \frac{306631}{863}e^{5} - 738e^{4} - \frac{389260}{863}e^{3} + \frac{648693}{863}e^{2} + \frac{255499}{863}e + \frac{14344}{863}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ $1$