Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 11
Level $[11,11,-4w + 23]$
Label 2.2.113.1-11.2-b
Dimension 9
CM no
Base change no

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Base field \(\Q(\sqrt{113}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[11,11,-4w + 23]$
Label 2.2.113.1-11.2-b
Dimension 9
Is CM no
Is base change no
Parent newspace dimension 27

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{9} \) \(\mathstrut +\mathstrut 4x^{8} \) \(\mathstrut -\mathstrut 6x^{7} \) \(\mathstrut -\mathstrut 35x^{6} \) \(\mathstrut +\mathstrut x^{5} \) \(\mathstrut +\mathstrut 90x^{4} \) \(\mathstrut +\mathstrut 31x^{3} \) \(\mathstrut -\mathstrut 67x^{2} \) \(\mathstrut -\mathstrut 29x \) \(\mathstrut -\mathstrut 3\)

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Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}\frac{13}{9}e^{8} + \frac{17}{3}e^{7} - \frac{28}{3}e^{6} - \frac{452}{9}e^{5} + 8e^{4} + 133e^{3} + \frac{223}{9}e^{2} - \frac{965}{9}e - \frac{70}{3}$
7 $[7, 7, 6w - 35]$ $\phantom{-}\frac{13}{9}e^{8} + \frac{17}{3}e^{7} - \frac{28}{3}e^{6} - \frac{452}{9}e^{5} + 8e^{4} + 132e^{3} + \frac{214}{9}e^{2} - \frac{929}{9}e - \frac{64}{3}$
7 $[7, 7, -6w - 29]$ $-\frac{19}{9}e^{8} - \frac{23}{3}e^{7} + \frac{46}{3}e^{6} + \frac{608}{9}e^{5} - 25e^{4} - 175e^{3} - \frac{94}{9}e^{2} + \frac{1211}{9}e + \frac{73}{3}$
9 $[9, 3, 3]$ $\phantom{-}\frac{7}{3}e^{8} + 9e^{7} - 16e^{6} - \frac{242}{3}e^{5} + 20e^{4} + 216e^{3} + \frac{82}{3}e^{2} - \frac{521}{3}e - 36$
11 $[11, 11, 4w + 19]$ $-\frac{16}{9}e^{8} - \frac{20}{3}e^{7} + \frac{37}{3}e^{6} + \frac{539}{9}e^{5} - 15e^{4} - 161e^{3} - \frac{226}{9}e^{2} + \frac{1178}{9}e + \frac{91}{3}$
11 $[11, 11, 4w - 23]$ $\phantom{-}1$
13 $[13, 13, -2w + 11]$ $-\frac{16}{9}e^{8} - \frac{20}{3}e^{7} + \frac{37}{3}e^{6} + \frac{530}{9}e^{5} - 17e^{4} - 154e^{3} - \frac{136}{9}e^{2} + \frac{1070}{9}e + \frac{70}{3}$
13 $[13, 13, 2w + 9]$ $\phantom{-}\frac{4}{9}e^{8} + \frac{5}{3}e^{7} - \frac{10}{3}e^{6} - \frac{146}{9}e^{5} + 5e^{4} + 49e^{3} + \frac{43}{9}e^{2} - \frac{407}{9}e - \frac{28}{3}$
25 $[25, 5, -5]$ $\phantom{-}\frac{4}{3}e^{8} + 5e^{7} - 9e^{6} - \frac{128}{3}e^{5} + 11e^{4} + 103e^{3} + \frac{43}{3}e^{2} - \frac{206}{3}e - 20$
31 $[31, 31, 2w - 13]$ $\phantom{-}\frac{1}{9}e^{8} + \frac{2}{3}e^{7} - \frac{4}{3}e^{6} - \frac{77}{9}e^{5} + 4e^{4} + 32e^{3} + \frac{4}{9}e^{2} - \frac{311}{9}e - \frac{16}{3}$
31 $[31, 31, -2w - 11]$ $\phantom{-}\frac{22}{3}e^{8} + 27e^{7} - 51e^{6} - \frac{710}{3}e^{5} + 69e^{4} + 611e^{3} + \frac{211}{3}e^{2} - \frac{1400}{3}e - 98$
41 $[41, 41, -8w - 39]$ $-\frac{28}{9}e^{8} - \frac{38}{3}e^{7} + \frac{58}{3}e^{6} + \frac{1022}{9}e^{5} - 11e^{4} - 306e^{3} - \frac{598}{9}e^{2} + \frac{2264}{9}e + \frac{175}{3}$
41 $[41, 41, 8w - 47]$ $-\frac{1}{3}e^{8} - 2e^{7} + e^{6} + \frac{59}{3}e^{5} + 8e^{4} - 61e^{3} - \frac{85}{3}e^{2} + \frac{170}{3}e + 16$
53 $[53, 53, -26w - 125]$ $-\frac{8}{9}e^{8} - \frac{10}{3}e^{7} + \frac{20}{3}e^{6} + \frac{283}{9}e^{5} - 11e^{4} - 90e^{3} - \frac{50}{9}e^{2} + \frac{679}{9}e + \frac{32}{3}$
53 $[53, 53, 26w - 151]$ $-\frac{37}{9}e^{8} - \frac{47}{3}e^{7} + \frac{82}{3}e^{6} + \frac{1247}{9}e^{5} - 27e^{4} - 364e^{3} - \frac{607}{9}e^{2} + \frac{2597}{9}e + \frac{202}{3}$
61 $[61, 61, -14w + 81]$ $-\frac{52}{9}e^{8} - \frac{65}{3}e^{7} + \frac{118}{3}e^{6} + \frac{1700}{9}e^{5} - 50e^{4} - 483e^{3} - \frac{496}{9}e^{2} + \frac{3293}{9}e + \frac{205}{3}$
61 $[61, 61, -14w - 67]$ $-\frac{13}{3}e^{8} - 18e^{7} + 26e^{6} + \frac{485}{3}e^{5} - 7e^{4} - 436e^{3} - \frac{325}{3}e^{2} + \frac{1064}{3}e + 78$
83 $[83, 83, 2w - 15]$ $-\frac{28}{3}e^{8} - 34e^{7} + 66e^{6} + \frac{899}{3}e^{5} - 95e^{4} - 781e^{3} - \frac{229}{3}e^{2} + \frac{1826}{3}e + 121$
83 $[83, 83, -2w - 13]$ $-\frac{61}{9}e^{8} - \frac{77}{3}e^{7} + \frac{139}{3}e^{6} + \frac{2042}{9}e^{5} - 56e^{4} - 591e^{3} - \frac{775}{9}e^{2} + \frac{4049}{9}e + \frac{298}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11,11,-4w + 23]$ $-1$