Properties

Label 2.2.120.1-15.1-h
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $15$
Level $[15, 15, w]$
Dimension $6$
CM no
Base change no

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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 $[101, 101, -7w + 37]$ $\phantom{-}\frac{6}{11}e^{5} + \frac{62}{11}e^{4} + \frac{155}{11}e^{3} - \frac{103}{11}e^{2} - \frac{392}{11}e + \frac{74}{11}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $-1$
$5$ $[5, 5, -w + 5]$ $1$