Properties

Label 2.2.229.1-3.1-c
Base field \(\Q(\sqrt{229}) \)
Weight $[2, 2]$
Level norm $3$
Level $[3, 3, w]$
Dimension $7$
CM no
Base change no

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Base field \(\Q(\sqrt{229}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[3, 3, w]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} - 3x^{6} - 11x^{5} + 42x^{4} - 7x^{3} - 76x^{2} + 56x - 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}\frac{17}{83}e^{6} + \frac{5}{83}e^{5} - \frac{234}{83}e^{4} - \frac{8}{83}e^{3} + \frac{670}{83}e^{2} + \frac{129}{83}e - \frac{327}{83}$
5 $[5, 5, w + 1]$ $-\frac{45}{83}e^{6} + \frac{60}{83}e^{5} + \frac{595}{83}e^{4} - \frac{926}{83}e^{3} - \frac{1173}{83}e^{2} + \frac{1714}{83}e - \frac{106}{83}$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{57}{83}e^{6} - \frac{76}{83}e^{5} - \frac{726}{83}e^{4} + \frac{1184}{83}e^{3} + \frac{1187}{83}e^{2} - \frac{2160}{83}e + \frac{588}{83}$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{56}{83}e^{6} - \frac{47}{83}e^{5} - \frac{722}{83}e^{4} + \frac{789}{83}e^{3} + \frac{1338}{83}e^{2} - \frac{1279}{83}e + \frac{534}{83}$
11 $[11, 11, w + 9]$ $\phantom{-}\frac{56}{83}e^{6} - \frac{47}{83}e^{5} - \frac{722}{83}e^{4} + \frac{789}{83}e^{3} + \frac{1421}{83}e^{2} - \frac{1113}{83}e - \frac{130}{83}$
17 $[17, 17, w + 2]$ $\phantom{-}\frac{21}{83}e^{6} - \frac{28}{83}e^{5} - \frac{250}{83}e^{4} + \frac{410}{83}e^{3} + \frac{232}{83}e^{2} - \frac{490}{83}e + \frac{221}{83}$
17 $[17, 17, w + 14]$ $\phantom{-}\frac{21}{83}e^{6} - \frac{28}{83}e^{5} - \frac{250}{83}e^{4} + \frac{410}{83}e^{3} + \frac{232}{83}e^{2} - \frac{407}{83}e + \frac{553}{83}$
19 $[19, 19, w]$ $-\frac{54}{83}e^{6} + \frac{72}{83}e^{5} + \frac{714}{83}e^{4} - \frac{1078}{83}e^{3} - \frac{1391}{83}e^{2} + \frac{1924}{83}e - \frac{260}{83}$
19 $[19, 19, w + 18]$ $-\frac{3}{83}e^{6} + \frac{4}{83}e^{5} + \frac{12}{83}e^{4} - \frac{106}{83}e^{3} + \frac{204}{83}e^{2} + \frac{236}{83}e - \frac{245}{83}$
37 $[37, 37, -w - 4]$ $\phantom{-}\frac{13}{83}e^{6} - \frac{45}{83}e^{5} - \frac{135}{83}e^{4} + \frac{653}{83}e^{3} - \frac{220}{83}e^{2} - \frac{1327}{83}e + \frac{1117}{83}$
37 $[37, 37, w - 5]$ $-\frac{89}{83}e^{6} + \frac{91}{83}e^{5} + \frac{1186}{83}e^{4} - \frac{1457}{83}e^{3} - \frac{2497}{83}e^{2} + \frac{2713}{83}e - \frac{241}{83}$
43 $[43, 43, w + 16]$ $\phantom{-}\frac{84}{83}e^{6} - \frac{195}{83}e^{5} - \frac{1000}{83}e^{4} + \frac{2802}{83}e^{3} + \frac{762}{83}e^{2} - \frac{5114}{83}e + \frac{1548}{83}$
43 $[43, 43, w + 26]$ $-\frac{13}{83}e^{6} + \frac{45}{83}e^{5} + \frac{135}{83}e^{4} - \frac{653}{83}e^{3} + \frac{137}{83}e^{2} + \frac{1161}{83}e - \frac{370}{83}$
49 $[49, 7, -7]$ $-\frac{79}{83}e^{6} + \frac{133}{83}e^{5} + \frac{980}{83}e^{4} - \frac{1989}{83}e^{3} - \frac{1268}{83}e^{2} + \frac{3697}{83}e - \frac{1527}{83}$
53 $[53, 53, -w - 10]$ $-\frac{41}{83}e^{6} + \frac{110}{83}e^{5} + \frac{496}{83}e^{4} - \frac{1504}{83}e^{3} - \frac{366}{83}e^{2} + \frac{2506}{83}e - \frac{803}{83}$
53 $[53, 53, w - 11]$ $\phantom{-}\frac{107}{83}e^{6} - \frac{198}{83}e^{5} - \frac{1341}{83}e^{4} + \frac{2923}{83}e^{3} + \frac{1771}{83}e^{2} - \frac{5623}{83}e + \frac{1794}{83}$
61 $[61, 61, w + 15]$ $-\frac{124}{83}e^{6} + \frac{193}{83}e^{5} + \frac{1575}{83}e^{4} - \frac{2832}{83}e^{3} - \frac{2441}{83}e^{2} + \frac{4664}{83}e - \frac{1135}{83}$
61 $[61, 61, w + 45]$ $-\frac{73}{83}e^{6} + \frac{125}{83}e^{5} + \frac{873}{83}e^{4} - \frac{1943}{83}e^{3} - \frac{929}{83}e^{2} + \frac{3972}{83}e - \frac{1120}{83}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$