Properties

Label 2.2.184.1-14.1-f
Base field \(\Q(\sqrt{46}) \)
Weight $[2, 2]$
Level norm $14$
Level $[14, 14, -3w - 20]$
Dimension $7$
CM no
Base change no

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Base field \(\Q(\sqrt{46}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[14, 14, -3w - 20]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $38$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} + x^{6} - 14x^{5} - 16x^{4} + 51x^{3} + 62x^{2} - 52x - 65\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, 23w - 156]$ $\phantom{-}1$
3 $[3, 3, -w - 7]$ $\phantom{-}e$
3 $[3, 3, w - 7]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{1}{2}e^{5} - 3e^{4} + 5e^{3} + \frac{35}{4}e^{2} - \frac{35}{4}e - \frac{31}{4}$
5 $[5, 5, -9w + 61]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{1}{2}e^{5} - 10e^{4} + 4e^{3} + \frac{141}{4}e^{2} - \frac{21}{4}e - \frac{149}{4}$
5 $[5, 5, -9w - 61]$ $-\frac{1}{4}e^{6} + \frac{1}{2}e^{5} + 3e^{4} - 5e^{3} - \frac{35}{4}e^{2} + \frac{35}{4}e + \frac{23}{4}$
7 $[7, 7, 4w - 27]$ $-1$
7 $[7, 7, 4w + 27]$ $-2e^{6} + e^{5} + 27e^{4} - 8e^{3} - 96e^{2} + 13e + 98$
23 $[23, 23, 78w - 529]$ $-\frac{3}{4}e^{6} + \frac{1}{2}e^{5} + 10e^{4} - 4e^{3} - \frac{137}{4}e^{2} + \frac{17}{4}e + \frac{129}{4}$
37 $[37, 37, -w - 3]$ $\phantom{-}5e^{6} - 3e^{5} - 66e^{4} + 25e^{3} + 225e^{2} - 41e - 221$
37 $[37, 37, w - 3]$ $-\frac{5}{4}e^{6} + \frac{1}{2}e^{5} + 18e^{4} - 4e^{3} - \frac{287}{4}e^{2} + \frac{19}{4}e + \frac{319}{4}$
41 $[41, 41, -2w + 15]$ $\phantom{-}\frac{21}{4}e^{6} - \frac{7}{2}e^{5} - 69e^{4} + 30e^{3} + \frac{931}{4}e^{2} - \frac{191}{4}e - \frac{875}{4}$
41 $[41, 41, 2w + 15]$ $\phantom{-}\frac{3}{2}e^{6} - 19e^{4} - 3e^{3} + \frac{113}{2}e^{2} + \frac{17}{2}e - \frac{83}{2}$
53 $[53, 53, -3w - 19]$ $-\frac{5}{4}e^{6} + \frac{1}{2}e^{5} + 18e^{4} - 4e^{3} - \frac{295}{4}e^{2} + \frac{27}{4}e + \frac{351}{4}$
53 $[53, 53, 3w - 19]$ $\phantom{-}\frac{21}{4}e^{6} - \frac{5}{2}e^{5} - 70e^{4} + 18e^{3} + \frac{967}{4}e^{2} - \frac{79}{4}e - \frac{951}{4}$
59 $[59, 59, 11w - 75]$ $-\frac{5}{4}e^{6} + \frac{1}{2}e^{5} + 17e^{4} - 3e^{3} - \frac{239}{4}e^{2} - \frac{5}{4}e + \frac{215}{4}$
59 $[59, 59, -11w - 75]$ $\phantom{-}\frac{39}{4}e^{6} - \frac{9}{2}e^{5} - 129e^{4} + 33e^{3} + \frac{1749}{4}e^{2} - \frac{177}{4}e - \frac{1669}{4}$
61 $[61, 61, -5w + 33]$ $\phantom{-}e^{6} - 15e^{4} - e^{3} + 63e^{2} - 78$
61 $[61, 61, 5w + 33]$ $-\frac{15}{2}e^{6} + 3e^{5} + 100e^{4} - 20e^{3} - \frac{687}{2}e^{2} + \frac{45}{2}e + \frac{657}{2}$
73 $[73, 73, -24w - 163]$ $-\frac{17}{2}e^{6} + 5e^{5} + 110e^{4} - 41e^{3} - \frac{717}{2}e^{2} + \frac{129}{2}e + \frac{665}{2}$
73 $[73, 73, -24w + 163]$ $\phantom{-}\frac{23}{4}e^{6} - \frac{5}{2}e^{5} - 78e^{4} + 19e^{3} + \frac{1117}{4}e^{2} - \frac{105}{4}e - \frac{1141}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, 23w - 156]$ $-1$
$7$ $[7, 7, 4w - 27]$ $1$