Properties

Base field 3.3.761.1
Weight [2, 2, 2]
Level norm 23
Level $[23, 23, -w^{2} + 2]$
Label 3.3.761.1-23.2-f
Dimension 8
CM no
Base change no

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Base field 3.3.761.1

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

Form

Weight [2, 2, 2]
Level $[23, 23, -w^{2} + 2]$
Label 3.3.761.1-23.2-f
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + 2x^{7} - 17x^{6} - 29x^{5} + 91x^{4} + 124x^{3} - 149x^{2} - 136x + 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{291}{5419}e^{7} + \frac{1372}{5419}e^{6} - \frac{2470}{5419}e^{5} - \frac{15908}{5419}e^{4} + \frac{3164}{5419}e^{3} + \frac{48100}{5419}e^{2} + \frac{555}{5419}e - \frac{24438}{5419}$
8 $[8, 2, 2]$ $-\frac{144}{5419}e^{7} - \frac{232}{5419}e^{6} + \frac{1334}{5419}e^{5} + \frac{2453}{5419}e^{4} + \frac{1898}{5419}e^{3} - \frac{7154}{5419}e^{2} - \frac{25135}{5419}e + \frac{3769}{5419}$
9 $[9, 3, -w^{2} + 2w + 4]$ $-\frac{13}{5419}e^{7} - \frac{322}{5419}e^{6} - \frac{858}{5419}e^{5} + \frac{2517}{5419}e^{4} + \frac{7773}{5419}e^{3} - \frac{119}{5419}e^{2} - \frac{10360}{5419}e - \frac{26115}{5419}$
11 $[11, 11, -w^{2} + 2w + 2]$ $-\frac{131}{5419}e^{7} + \frac{90}{5419}e^{6} + \frac{2192}{5419}e^{5} - \frac{64}{5419}e^{4} - \frac{11294}{5419}e^{3} - \frac{12454}{5419}e^{2} + \frac{17739}{5419}e + \frac{29884}{5419}$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{216}{5419}e^{7} - \frac{348}{5419}e^{6} + \frac{2001}{5419}e^{5} + \frac{970}{5419}e^{4} - \frac{2572}{5419}e^{3} + \frac{10945}{5419}e^{2} - \frac{7898}{5419}e - \frac{24151}{5419}$
19 $[19, 19, w + 3]$ $-\frac{409}{5419}e^{7} - \frac{960}{5419}e^{6} + \frac{5520}{5419}e^{5} + \frac{7908}{5419}e^{4} - \frac{27650}{5419}e^{3} - \frac{11664}{5419}e^{2} + \frac{54639}{5419}e + \frac{15409}{5419}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}\frac{658}{5419}e^{7} + \frac{458}{5419}e^{6} - \frac{10762}{5419}e^{5} - \frac{5263}{5419}e^{4} + \frac{52592}{5419}e^{3} + \frac{20196}{5419}e^{2} - \frac{73382}{5419}e - \frac{36264}{5419}$
19 $[19, 19, -w^{2} + 3w + 2]$ $-\frac{522}{5419}e^{7} - \frac{841}{5419}e^{6} + \frac{8900}{5419}e^{5} + \frac{12279}{5419}e^{4} - \frac{45955}{5419}e^{3} - \frac{48964}{5419}e^{2} + \frac{66714}{5419}e + \frac{30597}{5419}$
23 $[23, 23, w^{2} - w - 3]$ $-\frac{391}{5419}e^{7} - \frac{931}{5419}e^{6} + \frac{6708}{5419}e^{5} + \frac{12343}{5419}e^{4} - \frac{34661}{5419}e^{3} - \frac{47348}{5419}e^{2} + \frac{38137}{5419}e + \frac{44065}{5419}$
23 $[23, 23, -w^{2} + 2]$ $-1$
23 $[23, 23, -w + 4]$ $\phantom{-}\frac{316}{5419}e^{7} - \frac{93}{5419}e^{6} - \frac{6239}{5419}e^{5} + \frac{2595}{5419}e^{4} + \frac{34069}{5419}e^{3} - \frac{17116}{5419}e^{2} - \frac{41632}{5419}e + \frac{15362}{5419}$
31 $[31, 31, w^{2} - 5]$ $-\frac{844}{5419}e^{7} - \frac{2564}{5419}e^{6} + \frac{9324}{5419}e^{5} + \frac{26269}{5419}e^{4} - \frac{28916}{5419}e^{3} - \frac{61499}{5419}e^{2} + \frac{28949}{5419}e + \frac{16521}{5419}$
43 $[43, 43, w^{2} - 3w - 3]$ $\phantom{-}\frac{119}{5419}e^{7} + \frac{1697}{5419}e^{6} + \frac{2435}{5419}e^{5} - \frac{15537}{5419}e^{4} - \frac{27384}{5419}e^{3} + \frac{29018}{5419}e^{2} + \frac{34808}{5419}e - \frac{27312}{5419}$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}\frac{1090}{5419}e^{7} + \frac{1154}{5419}e^{6} - \frac{14764}{5419}e^{5} - \frac{7203}{5419}e^{4} + \frac{57736}{5419}e^{3} - \frac{7113}{5419}e^{2} - \frac{57586}{5419}e + \frac{28295}{5419}$
53 $[53, 53, 2w - 5]$ $\phantom{-}\frac{550}{5419}e^{7} + \frac{284}{5419}e^{6} - \frac{7052}{5419}e^{5} + \frac{641}{5419}e^{4} + \frac{18792}{5419}e^{3} - \frac{14974}{5419}e^{2} + \frac{20211}{5419}e - \frac{7697}{5419}$
61 $[61, 61, 2w^{2} - 2w - 9]$ $\phantom{-}\frac{870}{5419}e^{7} + \frac{3208}{5419}e^{6} - \frac{7608}{5419}e^{5} - \frac{31303}{5419}e^{4} + \frac{18789}{5419}e^{3} + \frac{72575}{5419}e^{2} - \frac{51581}{5419}e - \frac{56414}{5419}$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{1427}{5419}e^{7} + \frac{1998}{5419}e^{6} - \frac{19617}{5419}e^{5} - \frac{16594}{5419}e^{4} + \frac{80916}{5419}e^{3} + \frac{22650}{5419}e^{2} - \frac{100407}{5419}e + \frac{17480}{5419}$
73 $[73, 73, 2w^{2} - 5w - 5]$ $-\frac{64}{5419}e^{7} + \frac{499}{5419}e^{6} + \frac{6614}{5419}e^{5} - \frac{114}{5419}e^{4} - \frac{67195}{5419}e^{3} - \frac{21845}{5419}e^{2} + \frac{162839}{5419}e + \frac{28168}{5419}$
83 $[83, 83, w^{2} - w - 9]$ $-\frac{517}{5419}e^{7} - \frac{1134}{5419}e^{6} + \frac{9230}{5419}e^{5} + \frac{13812}{5419}e^{4} - \frac{50612}{5419}e^{3} - \frac{30577}{5419}e^{2} + \frac{61528}{5419}e - \frac{42728}{5419}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23, 23, -w^{2} + 2]$ $1$