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 | $[61, 61, 2w - 13]$ | $-\frac{5}{12}e^{8} - \frac{89}{12}e^{6} - \frac{118}{3}e^{4} - \frac{391}{6}e^{2} - \frac{70}{3}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).