Properties

Label 4.4.7232.1-23.2-c
Base field 4.4.7232.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23,23,w^{2} - w - 3]$
Dimension $10$
CM no
Base change no

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Base field 4.4.7232.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[23,23,w^{2} - w - 3]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 3x^{9} - 11x^{8} + 36x^{7} + 34x^{6} - 136x^{5} - 20x^{4} + 176x^{3} - 31x^{2} - 37x + 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$ $\phantom{-}\frac{11}{68}e^{9} - \frac{8}{17}e^{8} - \frac{127}{68}e^{7} + \frac{369}{68}e^{6} + \frac{457}{68}e^{5} - \frac{1303}{68}e^{4} - \frac{33}{4}e^{3} + \frac{1511}{68}e^{2} + \frac{14}{17}e - \frac{201}{68}$
2 $[2, 2, -w - 1]$ $\phantom{-}e$
17 $[17, 17, w^{2} - w - 5]$ $\phantom{-}\frac{7}{34}e^{9} - \frac{4}{17}e^{8} - \frac{87}{34}e^{7} + \frac{71}{34}e^{6} + \frac{365}{34}e^{5} - \frac{143}{34}e^{4} - \frac{39}{2}e^{3} + \frac{59}{34}e^{2} + \frac{245}{17}e - \frac{63}{34}$
17 $[17, 17, -\frac{1}{2}w^{3} + 2w^{2} + \frac{1}{2}w - 2]$ $\phantom{-}\frac{1}{17}e^{9} + \frac{11}{17}e^{8} - \frac{27}{17}e^{7} - \frac{138}{17}e^{6} + \frac{193}{17}e^{5} + \frac{543}{17}e^{4} - 26e^{3} - \frac{708}{17}e^{2} + \frac{223}{17}e + \frac{110}{17}$
23 $[23, 23, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}\frac{9}{17}e^{9} - \frac{20}{17}e^{8} - \frac{107}{17}e^{7} + \frac{220}{17}e^{6} + \frac{411}{17}e^{5} - \frac{723}{17}e^{4} - 36e^{3} + \frac{768}{17}e^{2} + \frac{273}{17}e - \frac{115}{17}$
23 $[23, 23, -w^{2} + w + 3]$ $-1$
41 $[41, 41, -w^{3} + 3w^{2} + 2w - 7]$ $-\frac{2}{17}e^{9} - \frac{5}{17}e^{8} + \frac{37}{17}e^{7} + \frac{72}{17}e^{6} - \frac{233}{17}e^{5} - \frac{338}{17}e^{4} + 34e^{3} + \frac{532}{17}e^{2} - \frac{480}{17}e - \frac{67}{17}$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w]$ $\phantom{-}\frac{1}{2}e^{9} - e^{8} - 6e^{7} + \frac{23}{2}e^{6} + \frac{45}{2}e^{5} - 40e^{4} - 27e^{3} + \frac{83}{2}e^{2} - e + 1$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ $\phantom{-}\frac{1}{17}e^{9} + \frac{5}{34}e^{8} - \frac{10}{17}e^{7} - \frac{53}{17}e^{6} + \frac{29}{34}e^{5} + \frac{661}{34}e^{4} + 6e^{3} - \frac{640}{17}e^{2} - \frac{557}{34}e + \frac{161}{17}$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w]$ $\phantom{-}\frac{7}{17}e^{9} - \frac{8}{17}e^{8} - \frac{104}{17}e^{7} + \frac{105}{17}e^{6} + \frac{518}{17}e^{5} - \frac{449}{17}e^{4} - 56e^{3} + \frac{637}{17}e^{2} + \frac{473}{17}e - \frac{97}{17}$
47 $[47, 47, \frac{3}{2}w^{3} - 4w^{2} - \frac{7}{2}w + 6]$ $-\frac{7}{34}e^{9} + \frac{25}{34}e^{8} + \frac{53}{34}e^{7} - \frac{275}{34}e^{6} + \frac{13}{17}e^{5} + \frac{454}{17}e^{4} - \frac{39}{2}e^{3} - \frac{977}{34}e^{2} + \frac{785}{34}e + \frac{165}{34}$
47 $[47, 47, w^{3} - w^{2} - 4w - 1]$ $\phantom{-}\frac{1}{17}e^{9} - \frac{6}{17}e^{8} - \frac{3}{34}e^{7} + \frac{66}{17}e^{6} - \frac{62}{17}e^{5} - \frac{461}{34}e^{4} + \frac{27}{2}e^{3} + \frac{312}{17}e^{2} - \frac{134}{17}e - \frac{69}{34}$
49 $[49, 7, w^{3} - 2w^{2} - 3w + 1]$ $-\frac{21}{34}e^{9} + \frac{12}{17}e^{8} + \frac{139}{17}e^{7} - \frac{247}{34}e^{6} - \frac{1197}{34}e^{5} + \frac{342}{17}e^{4} + 54e^{3} - \frac{415}{34}e^{2} - \frac{293}{17}e - \frac{16}{17}$
49 $[49, 7, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}\frac{3}{34}e^{9} - \frac{9}{17}e^{8} - \frac{13}{34}e^{7} + \frac{215}{34}e^{6} - \frac{67}{34}e^{5} - \frac{819}{34}e^{4} + \frac{11}{2}e^{3} + \frac{1123}{34}e^{2} + \frac{71}{17}e - \frac{197}{34}$
71 $[71, 71, \frac{5}{2}w^{3} - 6w^{2} - \frac{17}{2}w + 12]$ $-\frac{1}{2}e^{9} + e^{8} + \frac{13}{2}e^{7} - \frac{25}{2}e^{6} - \frac{55}{2}e^{5} + \frac{99}{2}e^{4} + \frac{81}{2}e^{3} - \frac{131}{2}e^{2} - 7e + \frac{31}{2}$
71 $[71, 71, 2w^{2} - 4w - 7]$ $\phantom{-}\frac{15}{34}e^{9} - \frac{11}{17}e^{8} - \frac{201}{34}e^{7} + \frac{293}{34}e^{6} + \frac{855}{34}e^{5} - \frac{1273}{34}e^{4} - \frac{69}{2}e^{3} + \frac{1909}{34}e^{2} + \frac{66}{17}e - \frac{407}{34}$
73 $[73, 73, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{29}{34}e^{9} - \frac{36}{17}e^{8} - \frac{341}{34}e^{7} + \frac{809}{34}e^{6} + \frac{1245}{34}e^{5} - \frac{2715}{34}e^{4} - \frac{89}{2}e^{3} + \frac{2809}{34}e^{2} + \frac{80}{17}e - \frac{159}{34}$
73 $[73, 73, 2w - 1]$ $\phantom{-}\frac{10}{17}e^{9} - \frac{9}{17}e^{8} - \frac{285}{34}e^{7} + \frac{116}{17}e^{6} + \frac{655}{17}e^{5} - \frac{989}{34}e^{4} - \frac{119}{2}e^{3} + \frac{740}{17}e^{2} + \frac{258}{17}e - \frac{367}{34}$
79 $[79, 79, \frac{3}{2}w^{3} - 4w^{2} - \frac{11}{2}w + 12]$ $\phantom{-}\frac{12}{17}e^{9} - \frac{21}{17}e^{8} - \frac{291}{34}e^{7} + \frac{231}{17}e^{6} + \frac{565}{17}e^{5} - \frac{1537}{34}e^{4} - \frac{97}{2}e^{3} + \frac{905}{17}e^{2} + \frac{330}{17}e - \frac{607}{34}$
79 $[79, 79, -w^{2} - w - 1]$ $-\frac{35}{34}e^{9} + \frac{37}{17}e^{8} + \frac{435}{34}e^{7} - \frac{865}{34}e^{6} - \frac{1757}{34}e^{5} + \frac{3095}{34}e^{4} + \frac{155}{2}e^{3} - \frac{3525}{34}e^{2} - \frac{511}{17}e + \frac{485}{34}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23,23,w^{2} - w - 3]$ $1$