Properties

Base field \(\Q(\sqrt{67}) \)
Weight [2, 2]
Level norm 12
Level $[12, 6, -2w + 16]$
Label 2.2.268.1-12.1-d
Dimension 9
CM no
Base change no

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{67}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[12, 6, -2w + 16]$
Label 2.2.268.1-12.1-d
Dimension 9
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{9} \) \(\mathstrut +\mathstrut 6x^{8} \) \(\mathstrut -\mathstrut 57x^{6} \) \(\mathstrut -\mathstrut 82x^{5} \) \(\mathstrut +\mathstrut 82x^{4} \) \(\mathstrut +\mathstrut 186x^{3} \) \(\mathstrut +\mathstrut 7x^{2} \) \(\mathstrut -\mathstrut 102x \) \(\mathstrut -\mathstrut 38\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $\phantom{-}0$
3 $[3, 3, -w + 8]$ $-1$
3 $[3, 3, -w - 8]$ $\phantom{-}e$
7 $[7, 7, -11w + 90]$ $-\frac{18}{43}e^{8} - \frac{100}{43}e^{7} + \frac{54}{43}e^{6} + \frac{1045}{43}e^{5} + \frac{959}{43}e^{4} - \frac{2294}{43}e^{3} - \frac{2510}{43}e^{2} + \frac{1453}{43}e + \frac{1324}{43}$
7 $[7, 7, -11w - 90]$ $\phantom{-}\frac{19}{43}e^{8} + \frac{96}{43}e^{7} - \frac{100}{43}e^{6} - \frac{1029}{43}e^{5} - \frac{556}{43}e^{4} + \frac{2431}{43}e^{3} + \frac{1627}{43}e^{2} - \frac{1646}{43}e - \frac{958}{43}$
11 $[11, 11, 6w - 49]$ $\phantom{-}\frac{1}{43}e^{8} - \frac{4}{43}e^{7} - \frac{46}{43}e^{6} - \frac{27}{43}e^{5} + \frac{317}{43}e^{4} + \frac{524}{43}e^{3} - \frac{152}{43}e^{2} - \frac{580}{43}e - \frac{236}{43}$
11 $[11, 11, 6w + 49]$ $-\frac{47}{43}e^{8} - \frac{242}{43}e^{7} + \frac{184}{43}e^{6} + \frac{2473}{43}e^{5} + \frac{2000}{43}e^{4} - \frac{5063}{43}e^{3} - \frac{5111}{43}e^{2} + \frac{3051}{43}e + \frac{2664}{43}$
17 $[17, 17, 4w + 33]$ $\phantom{-}\frac{36}{43}e^{8} + \frac{200}{43}e^{7} - \frac{108}{43}e^{6} - \frac{2047}{43}e^{5} - \frac{1832}{43}e^{4} + \frac{4158}{43}e^{3} + \frac{4289}{43}e^{2} - \frac{2261}{43}e - \frac{2089}{43}$
17 $[17, 17, -4w + 33]$ $-\frac{8}{43}e^{8} - \frac{54}{43}e^{7} - \frac{19}{43}e^{6} + \frac{517}{43}e^{5} + \frac{818}{43}e^{4} - \frac{838}{43}e^{3} - \frac{1579}{43}e^{2} + \frac{512}{43}e + \frac{641}{43}$
25 $[25, 5, -5]$ $\phantom{-}\frac{60}{43}e^{8} + \frac{319}{43}e^{7} - \frac{223}{43}e^{6} - \frac{3254}{43}e^{5} - \frac{2566}{43}e^{4} + \frac{6586}{43}e^{3} + \frac{5887}{43}e^{2} - \frac{3754}{43}e - \frac{2808}{43}$
29 $[29, 29, -70w + 573]$ $\phantom{-}\frac{83}{43}e^{8} + \frac{442}{43}e^{7} - \frac{292}{43}e^{6} - \frac{4520}{43}e^{5} - \frac{3832}{43}e^{4} + \frac{9264}{43}e^{3} + \frac{9443}{43}e^{2} - \frac{5570}{43}e - \frac{4925}{43}$
29 $[29, 29, 151w - 1236]$ $-\frac{38}{43}e^{8} - \frac{192}{43}e^{7} + \frac{200}{43}e^{6} + \frac{2058}{43}e^{5} + \frac{1112}{43}e^{4} - \frac{4862}{43}e^{3} - \frac{3297}{43}e^{2} + \frac{3249}{43}e + \frac{2045}{43}$
31 $[31, 31, -w - 6]$ $-\frac{71}{43}e^{8} - \frac{361}{43}e^{7} + \frac{299}{43}e^{6} + \frac{3680}{43}e^{5} + \frac{2734}{43}e^{4} - \frac{7448}{43}e^{3} - \frac{6666}{43}e^{2} + \frac{4286}{43}e + \frac{3340}{43}$
31 $[31, 31, w - 6]$ $-\frac{16}{43}e^{8} - \frac{108}{43}e^{7} + \frac{5}{43}e^{6} + \frac{1163}{43}e^{5} + \frac{1335}{43}e^{4} - \frac{2794}{43}e^{3} - \frac{3502}{43}e^{2} + \frac{2099}{43}e + \frac{1970}{43}$
37 $[37, 37, -21w - 172]$ $-\frac{66}{43}e^{8} - \frac{338}{43}e^{7} + \frac{284}{43}e^{6} + \frac{3502}{43}e^{5} + \frac{2556}{43}e^{4} - \frac{7451}{43}e^{3} - \frac{6738}{43}e^{2} + \frac{4439}{43}e + \frac{3751}{43}$
37 $[37, 37, -21w + 172]$ $\phantom{-}\frac{66}{43}e^{8} + \frac{338}{43}e^{7} - \frac{284}{43}e^{6} - \frac{3459}{43}e^{5} - \frac{2470}{43}e^{4} + \frac{7064}{43}e^{3} + \frac{6050}{43}e^{2} - \frac{4095}{43}e - \frac{3235}{43}$
43 $[43, 43, 2w - 15]$ $\phantom{-}\frac{24}{43}e^{8} + \frac{119}{43}e^{7} - \frac{115}{43}e^{6} - \frac{1250}{43}e^{5} - \frac{863}{43}e^{4} + \frac{2772}{43}e^{3} + \frac{2673}{43}e^{2} - \frac{1622}{43}e - \frac{1794}{43}$
43 $[43, 43, 2w + 15]$ $\phantom{-}\frac{63}{43}e^{8} + \frac{350}{43}e^{7} - \frac{189}{43}e^{6} - \frac{3593}{43}e^{5} - \frac{3206}{43}e^{4} + \frac{7470}{43}e^{3} + \frac{7538}{43}e^{2} - \frac{4720}{43}e - \frac{3860}{43}$
67 $[67, 67, -w]$ $\phantom{-}\frac{50}{43}e^{8} + \frac{273}{43}e^{7} - \frac{150}{43}e^{6} - \frac{2726}{43}e^{5} - \frac{2468}{43}e^{4} + \frac{5087}{43}e^{3} + \frac{5300}{43}e^{2} - \frac{2641}{43}e - \frac{2426}{43}$
73 $[73, 73, -3w - 26]$ $-\frac{7}{43}e^{8} - \frac{15}{43}e^{7} + \frac{107}{43}e^{6} + \frac{189}{43}e^{5} - \frac{499}{43}e^{4} - \frac{615}{43}e^{3} + \frac{634}{43}e^{2} + \frac{448}{43}e + \frac{233}{43}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $-1$
3 $[3, 3, -w + 8]$ $1$