Properties

Label 2.2.205.1-1.1-d
Base field \(\Q(\sqrt{205}) \)
Weight $[2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $10$
CM no
Base change no

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Base field \(\Q(\sqrt{205}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[1, 1, 1]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} + 20x^{8} + 135x^{6} + 378x^{4} + 426x^{2} + 128\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-e$
4 $[4, 2, 2]$ $-\frac{5}{24}e^{8} - \frac{89}{24}e^{6} - \frac{121}{6}e^{4} - \frac{439}{12}e^{2} - \frac{41}{3}$
5 $[5, 5, -w + 8]$ $-\frac{1}{4}e^{8} - \frac{17}{4}e^{6} - 21e^{4} - \frac{61}{2}e^{2} - 6$
7 $[7, 7, w + 1]$ $\phantom{-}\frac{5}{24}e^{9} + \frac{89}{24}e^{7} + \frac{121}{6}e^{5} + \frac{451}{12}e^{3} + \frac{59}{3}e$
7 $[7, 7, w + 5]$ $-\frac{5}{24}e^{9} - \frac{89}{24}e^{7} - \frac{121}{6}e^{5} - \frac{451}{12}e^{3} - \frac{59}{3}e$
13 $[13, 13, w + 3]$ $\phantom{-}\frac{13}{24}e^{9} + \frac{229}{24}e^{7} + \frac{151}{3}e^{5} + \frac{1007}{12}e^{3} + \frac{79}{3}e$
13 $[13, 13, w + 9]$ $-\frac{13}{24}e^{9} - \frac{229}{24}e^{7} - \frac{151}{3}e^{5} - \frac{1007}{12}e^{3} - \frac{79}{3}e$
17 $[17, 17, w]$ $-\frac{1}{2}e^{9} - 9e^{7} - \frac{99}{2}e^{5} - 91e^{3} - 41e$
17 $[17, 17, w + 16]$ $\phantom{-}\frac{1}{2}e^{9} + 9e^{7} + \frac{99}{2}e^{5} + 91e^{3} + 41e$
31 $[31, 31, -w - 4]$ $\phantom{-}\frac{37}{24}e^{8} + \frac{649}{24}e^{6} + \frac{851}{6}e^{4} + \frac{2831}{12}e^{2} + \frac{232}{3}$
31 $[31, 31, w - 5]$ $\phantom{-}\frac{37}{24}e^{8} + \frac{649}{24}e^{6} + \frac{851}{6}e^{4} + \frac{2831}{12}e^{2} + \frac{232}{3}$
41 $[41, 41, 3w - 22]$ $\phantom{-}\frac{5}{4}e^{8} + \frac{89}{4}e^{6} + 119e^{4} + \frac{399}{2}e^{2} + 58$
47 $[47, 47, w + 19]$ $\phantom{-}\frac{7}{8}e^{9} + \frac{123}{8}e^{7} + \frac{161}{2}e^{5} + \frac{525}{4}e^{3} + 39e$
47 $[47, 47, w + 27]$ $-\frac{7}{8}e^{9} - \frac{123}{8}e^{7} - \frac{161}{2}e^{5} - \frac{525}{4}e^{3} - 39e$
53 $[53, 53, w + 14]$ $\phantom{-}\frac{1}{4}e^{9} + \frac{19}{4}e^{7} + \frac{57}{2}e^{5} + \frac{119}{2}e^{3} + 31e$
53 $[53, 53, w + 38]$ $-\frac{1}{4}e^{9} - \frac{19}{4}e^{7} - \frac{57}{2}e^{5} - \frac{119}{2}e^{3} - 31e$
59 $[59, 59, -w - 10]$ $\phantom{-}\frac{7}{8}e^{8} + \frac{123}{8}e^{6} + \frac{161}{2}e^{4} + \frac{525}{4}e^{2} + 36$
59 $[59, 59, w - 11]$ $\phantom{-}\frac{7}{8}e^{8} + \frac{123}{8}e^{6} + \frac{161}{2}e^{4} + \frac{525}{4}e^{2} + 36$
61 $[61, 61, 2w - 13]$ $-\frac{5}{12}e^{8} - \frac{89}{12}e^{6} - \frac{118}{3}e^{4} - \frac{391}{6}e^{2} - \frac{70}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).