Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[15, 15, w]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 13x^{5} + 54x^{4} + 56x^{3} - 105x^{2} - 168x + 28\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}\frac{3}{11}e^{5} + \frac{31}{11}e^{4} + \frac{83}{11}e^{3} - \frac{24}{11}e^{2} - \frac{196}{11}e + \frac{4}{11}$ |
3 | $[3, 3, w]$ | $\phantom{-}1$ |
5 | $[5, 5, -w + 5]$ | $-1$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 4]$ | $-\frac{7}{11}e^{5} - \frac{76}{11}e^{4} - \frac{212}{11}e^{3} + \frac{78}{11}e^{2} + \frac{549}{11}e - \frac{112}{11}$ |
13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{4}{11}e^{5} + \frac{45}{11}e^{4} + \frac{129}{11}e^{3} - \frac{43}{11}e^{2} - \frac{320}{11}e + \frac{20}{11}$ |
13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{13}{11}e^{5} + \frac{138}{11}e^{4} + \frac{378}{11}e^{3} - \frac{137}{11}e^{2} - \frac{996}{11}e + \frac{76}{11}$ |
17 | $[17, 17, w + 8]$ | $\phantom{-}\frac{9}{11}e^{5} + \frac{93}{11}e^{4} + \frac{238}{11}e^{3} - \frac{149}{11}e^{2} - \frac{654}{11}e + \frac{188}{11}$ |
17 | $[17, 17, w + 9]$ | $-\frac{19}{11}e^{5} - \frac{200}{11}e^{4} - \frac{533}{11}e^{3} + \frac{251}{11}e^{2} + \frac{1410}{11}e - \frac{260}{11}$ |
19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{3}{11}e^{5} + \frac{31}{11}e^{4} + \frac{72}{11}e^{3} - \frac{90}{11}e^{2} - \frac{240}{11}e + \frac{114}{11}$ |
19 | $[19, 19, -w + 7]$ | $-\frac{2}{11}e^{5} - \frac{17}{11}e^{4} - \frac{26}{11}e^{3} + \frac{60}{11}e^{2} + \frac{72}{11}e - \frac{54}{11}$ |
29 | $[29, 29, -w - 1]$ | $-\frac{9}{11}e^{5} - \frac{93}{11}e^{4} - \frac{249}{11}e^{3} + \frac{83}{11}e^{2} + \frac{632}{11}e - \frac{34}{11}$ |
29 | $[29, 29, w - 1]$ | $-e^{2} - 4e + 2$ |
37 | $[37, 37, w + 17]$ | $\phantom{-}\frac{6}{11}e^{5} + \frac{62}{11}e^{4} + \frac{155}{11}e^{3} - \frac{114}{11}e^{2} - \frac{414}{11}e + \frac{184}{11}$ |
37 | $[37, 37, w + 20]$ | $-\frac{13}{11}e^{5} - \frac{138}{11}e^{4} - \frac{367}{11}e^{3} + \frac{192}{11}e^{2} + \frac{974}{11}e - \frac{208}{11}$ |
71 | $[71, 71, 2w - 7]$ | $-\frac{19}{11}e^{5} - \frac{200}{11}e^{4} - \frac{533}{11}e^{3} + \frac{251}{11}e^{2} + \frac{1388}{11}e - \frac{304}{11}$ |
71 | $[71, 71, -2w - 7]$ | $\phantom{-}\frac{23}{11}e^{5} + \frac{245}{11}e^{4} + \frac{662}{11}e^{3} - \frac{305}{11}e^{2} - \frac{1752}{11}e + \frac{368}{11}$ |
83 | $[83, 83, w + 14]$ | $-\frac{43}{11}e^{5} - \frac{448}{11}e^{4} - \frac{1186}{11}e^{3} + \frac{542}{11}e^{2} + \frac{3154}{11}e - \frac{468}{11}$ |
83 | $[83, 83, w + 69]$ | $\phantom{-}\frac{17}{11}e^{5} + \frac{172}{11}e^{4} + \frac{430}{11}e^{3} - \frac{290}{11}e^{2} - \frac{1250}{11}e + \frac{316}{11}$ |
101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{6}{11}e^{5} + \frac{62}{11}e^{4} + \frac{155}{11}e^{3} - \frac{103}{11}e^{2} - \frac{392}{11}e + \frac{74}{11}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $-1$ |
$5$ | $[5, 5, -w + 5]$ | $1$ |