Properties

Label 4.4.18097.1-7.1-b
Base field 4.4.18097.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$
Dimension $12$
CM no
Base change no

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Base field 4.4.18097.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 29x^{10} + 308x^{8} - 1435x^{6} + 2617x^{4} - 820x^{2} + 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $\phantom{-}\frac{283}{9456}e^{11} - \frac{2765}{3152}e^{9} + \frac{22085}{2364}e^{7} - \frac{134835}{3152}e^{5} + \frac{679579}{9456}e^{3} - \frac{17621}{2364}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $\phantom{-}\frac{305}{9456}e^{11} - \frac{2863}{3152}e^{9} + \frac{21985}{2364}e^{7} - \frac{130537}{3152}e^{5} + \frac{672281}{9456}e^{3} - \frac{42493}{2364}e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-1$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $-\frac{109}{2364}e^{10} + \frac{987}{788}e^{8} - \frac{7295}{591}e^{6} + \frac{41817}{788}e^{4} - \frac{206689}{2364}e^{2} + \frac{7286}{591}$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $\phantom{-}\frac{167}{1576}e^{11} - \frac{4739}{1576}e^{9} + \frac{12225}{394}e^{7} - \frac{218469}{1576}e^{5} + \frac{367471}{1576}e^{3} - \frac{15459}{394}e$
27 $[27, 3, -w^{3} + 7w + 1]$ $\phantom{-}e^{3} - 9e$
31 $[31, 31, w + 3]$ $\phantom{-}\frac{103}{2364}e^{10} - \frac{817}{788}e^{8} + \frac{5012}{591}e^{6} - \frac{22143}{788}e^{4} + \frac{79519}{2364}e^{2} - \frac{3404}{591}$
31 $[31, 31, -w^{2} + 5]$ $-\frac{275}{4728}e^{11} + \frac{2801}{1576}e^{9} - \frac{11786}{591}e^{7} + \frac{154307}{1576}e^{5} - \frac{873287}{4728}e^{3} + \frac{27794}{591}e$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}\frac{113}{1576}e^{11} - \frac{3301}{1576}e^{9} + \frac{8817}{394}e^{7} - \frac{164011}{1576}e^{5} + \frac{289105}{1576}e^{3} - \frac{15193}{394}e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}\frac{49}{788}e^{11} - \frac{1407}{788}e^{9} + \frac{7345}{394}e^{7} - \frac{66343}{788}e^{5} + \frac{111867}{788}e^{3} - \frac{6867}{394}e$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}\frac{73}{1576}e^{11} - \frac{2265}{1576}e^{9} + \frac{3201}{197}e^{7} - \frac{125131}{1576}e^{5} + \frac{231669}{1576}e^{3} - \frac{7954}{197}e$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $-\frac{8}{591}e^{11} + \frac{125}{394}e^{9} - \frac{2879}{1182}e^{7} + \frac{1213}{197}e^{5} + \frac{1493}{1182}e^{3} - \frac{11191}{1182}e$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}\frac{3}{197}e^{10} - \frac{58}{197}e^{8} + \frac{232}{197}e^{6} + \frac{1024}{197}e^{4} - \frac{5956}{197}e^{2} + \frac{2086}{197}$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $-\frac{527}{4728}e^{11} + \frac{5213}{1576}e^{9} - \frac{21314}{591}e^{7} + \frac{271415}{1576}e^{5} - \frac{1486427}{4728}e^{3} + \frac{40169}{591}e$
83 $[83, 83, -w^{3} + 5w + 1]$ $-\frac{28}{197}e^{10} + \frac{804}{197}e^{8} - \frac{8338}{197}e^{6} + \frac{37066}{197}e^{4} - \frac{61363}{197}e^{2} + \frac{10212}{197}$
83 $[83, 83, 2w - 1]$ $\phantom{-}\frac{437}{2364}e^{11} - \frac{4239}{788}e^{9} + \frac{33796}{591}e^{7} - \frac{207977}{788}e^{5} + \frac{1077653}{2364}e^{3} - \frac{38065}{591}e$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $-\frac{65}{2364}e^{10} + \frac{791}{788}e^{8} - \frac{7495}{591}e^{6} + \frac{51989}{788}e^{4} - \frac{292205}{2364}e^{2} + \frac{17824}{591}$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $\phantom{-}\frac{115}{2364}e^{10} - \frac{1157}{788}e^{8} + \frac{9578}{591}e^{6} - \frac{61491}{788}e^{4} + \frac{338587}{2364}e^{2} - \frac{17078}{591}$
89 $[89, 89, w^{3} - 5w + 5]$ $-\frac{23}{197}e^{10} + \frac{576}{197}e^{8} - \frac{5062}{197}e^{6} + \frac{18613}{197}e^{4} - \frac{25323}{197}e^{2} + \frac{3970}{197}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $1$