Properties

Base field \(\Q(\sqrt{67}) \)
Weight [2, 2]
Level norm 6
Level $[6,6,-5w + 41]$
Label 2.2.268.1-6.2-i
Dimension 8
CM no
Base change no

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Base field \(\Q(\sqrt{67}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[6,6,-5w + 41]$
Label 2.2.268.1-6.2-i
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 24

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut +\mathstrut x^{7} \) \(\mathstrut -\mathstrut 20x^{6} \) \(\mathstrut -\mathstrut 17x^{5} \) \(\mathstrut +\mathstrut 129x^{4} \) \(\mathstrut +\mathstrut 85x^{3} \) \(\mathstrut -\mathstrut 296x^{2} \) \(\mathstrut -\mathstrut 109x \) \(\mathstrut +\mathstrut 194\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $-1$
3 $[3, 3, -w + 8]$ $\phantom{-}e$
3 $[3, 3, -w - 8]$ $-1$
7 $[7, 7, -11w + 90]$ $-\frac{27}{538}e^{7} - \frac{11}{538}e^{6} + \frac{417}{538}e^{5} + \frac{91}{269}e^{4} - \frac{834}{269}e^{3} - \frac{1187}{538}e^{2} + \frac{502}{269}e + \frac{910}{269}$
7 $[7, 7, -11w - 90]$ $\phantom{-}\frac{77}{1076}e^{7} - \frac{69}{538}e^{6} - \frac{759}{538}e^{5} + \frac{2161}{1076}e^{4} + \frac{4381}{538}e^{3} - \frac{8949}{1076}e^{2} - \frac{13693}{1076}e + \frac{4349}{538}$
11 $[11, 11, 6w - 49]$ $-\frac{25}{1076}e^{7} - \frac{15}{269}e^{6} + \frac{104}{269}e^{5} + \frac{577}{1076}e^{4} - \frac{1101}{538}e^{3} - \frac{43}{1076}e^{2} + \frac{3251}{1076}e - \frac{1419}{538}$
11 $[11, 11, 6w + 49]$ $\phantom{-}\frac{39}{538}e^{7} - \frac{7}{269}e^{6} - \frac{346}{269}e^{5} + \frac{305}{538}e^{4} + \frac{1922}{269}e^{3} - \frac{1633}{538}e^{2} - \frac{6621}{538}e + \frac{987}{269}$
17 $[17, 17, 4w + 33]$ $-\frac{11}{538}e^{7} - \frac{67}{269}e^{6} + \frac{70}{269}e^{5} + \frac{1997}{538}e^{4} - \frac{280}{269}e^{3} - \frac{8175}{538}e^{2} + \frac{957}{538}e + \frac{4067}{269}$
17 $[17, 17, -4w + 33]$ $\phantom{-}\frac{25}{1076}e^{7} + \frac{15}{269}e^{6} - \frac{104}{269}e^{5} - \frac{577}{1076}e^{4} + \frac{1101}{538}e^{3} + \frac{43}{1076}e^{2} - \frac{4327}{1076}e + \frac{2495}{538}$
25 $[25, 5, -5]$ $-\frac{21}{1076}e^{7} - \frac{79}{538}e^{6} + \frac{207}{538}e^{5} + \frac{2443}{1076}e^{4} - \frac{1097}{538}e^{3} - \frac{9591}{1076}e^{2} + \frac{2365}{1076}e + \frac{3607}{538}$
29 $[29, 29, -70w + 573]$ $-\frac{29}{1076}e^{7} + \frac{19}{538}e^{6} + \frac{209}{538}e^{5} - \frac{1289}{1076}e^{4} - \frac{567}{538}e^{3} + \frac{9505}{1076}e^{2} - \frac{1243}{1076}e - \frac{5907}{538}$
29 $[29, 29, 151w - 1236]$ $-\frac{25}{538}e^{7} - \frac{30}{269}e^{6} + \frac{208}{269}e^{5} + \frac{1115}{538}e^{4} - \frac{832}{269}e^{3} - \frac{5961}{538}e^{2} + \frac{561}{538}e + \frac{3423}{269}$
31 $[31, 31, -w - 6]$ $-\frac{33}{269}e^{7} + \frac{3}{538}e^{6} + \frac{1109}{538}e^{5} - \frac{123}{538}e^{4} - \frac{2487}{269}e^{3} + \frac{223}{269}e^{2} + \frac{3859}{538}e - \frac{77}{269}$
31 $[31, 31, w - 6]$ $-\frac{79}{1076}e^{7} - \frac{41}{538}e^{6} + \frac{625}{538}e^{5} + \frac{941}{1076}e^{4} - \frac{2769}{538}e^{3} - \frac{2417}{1076}e^{2} + \frac{8487}{1076}e + \frac{401}{538}$
37 $[37, 37, -21w - 172]$ $\phantom{-}\frac{41}{1076}e^{7} + \frac{103}{538}e^{6} - \frac{481}{538}e^{5} - \frac{3335}{1076}e^{4} + \frac{3269}{538}e^{3} + \frac{13499}{1076}e^{2} - \frac{11637}{1076}e - \frac{3225}{538}$
37 $[37, 37, -21w + 172]$ $\phantom{-}\frac{1}{269}e^{7} - \frac{49}{538}e^{6} - \frac{1}{538}e^{5} + \frac{933}{538}e^{4} + \frac{2}{269}e^{3} - \frac{2656}{269}e^{2} - \frac{1519}{538}e + \frac{4665}{269}$
43 $[43, 43, 2w - 15]$ $\phantom{-}\frac{38}{269}e^{7} + \frac{21}{538}e^{6} - \frac{1383}{538}e^{5} - \frac{323}{538}e^{4} + \frac{3573}{269}e^{3} + \frac{485}{269}e^{2} - \frac{7957}{538}e + \frac{1075}{269}$
43 $[43, 43, 2w + 15]$ $-\frac{103}{1076}e^{7} - \frac{8}{269}e^{6} + \frac{450}{269}e^{5} + \frac{1043}{1076}e^{4} - \frac{4407}{538}e^{3} - \frac{6461}{1076}e^{2} + \frac{10037}{1076}e + \frac{373}{538}$
67 $[67, 67, -w]$ $-\frac{181}{1076}e^{7} - \frac{1}{269}e^{6} + \frac{796}{269}e^{5} - \frac{643}{1076}e^{4} - \frac{7713}{538}e^{3} + \frac{6489}{1076}e^{2} + \frac{16823}{1076}e - \frac{5367}{538}$
73 $[73, 73, -3w - 26]$ $\phantom{-}\frac{237}{1076}e^{7} + \frac{123}{538}e^{6} - \frac{1875}{538}e^{5} - \frac{3899}{1076}e^{4} + \frac{8307}{538}e^{3} + \frac{16935}{1076}e^{2} - \frac{19005}{1076}e - \frac{6045}{538}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,27w + 221]$ $1$
3 $[3,3,w + 8]$ $1$