Properties

Label 6.6.1279733.1-41.1-g
Base field 6.6.1279733.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$
Dimension $16$
CM no
Base change no

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Base field 6.6.1279733.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$
Dimension: $16$
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:

\(x^{16} - 80x^{14} + 2560x^{12} - 41264x^{10} + 342592x^{8} - 1292800x^{6} + 1353728x^{4} - 307200x^{2} + 16384\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ $\phantom{-}e$
7 $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ $-\frac{3}{32768}e^{15} + \frac{53}{8192}e^{13} - \frac{371}{2048}e^{11} + \frac{5197}{2048}e^{9} - \frac{4697}{256}e^{7} + \frac{499}{8}e^{5} - \frac{1163}{16}e^{3} + \frac{167}{8}e$
13 $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{4096}e^{14} - \frac{1}{64}e^{12} + \frac{195}{512}e^{10} - \frac{1113}{256}e^{8} + \frac{1453}{64}e^{6} - \frac{1405}{32}e^{4} + \frac{57}{2}e^{2} - \frac{3}{2}$
29 $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ $\phantom{-}\frac{5}{65536}e^{15} - \frac{117}{16384}e^{13} + \frac{1065}{4096}e^{11} - \frac{19059}{4096}e^{9} + \frac{10701}{256}e^{7} - \frac{20991}{128}e^{5} + 150e^{3} - \frac{207}{16}e$
29 $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ $-\frac{13}{65536}e^{15} + \frac{241}{16384}e^{13} - \frac{1781}{4096}e^{11} + \frac{26443}{4096}e^{9} - \frac{3153}{64}e^{7} + \frac{21831}{128}e^{5} - \frac{2597}{16}e^{3} + \frac{535}{16}e$
29 $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ $\phantom{-}\frac{3}{65536}e^{15} - \frac{39}{16384}e^{13} + \frac{151}{4096}e^{11} + \frac{11}{4096}e^{9} - \frac{587}{128}e^{7} + \frac{4169}{128}e^{5} - \frac{747}{16}e^{3} + \frac{307}{16}e$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}\frac{23}{65536}e^{15} - \frac{491}{16384}e^{13} + \frac{4163}{4096}e^{11} - \frac{70561}{4096}e^{9} + \frac{19057}{128}e^{7} - \frac{73463}{128}e^{5} + \frac{8985}{16}e^{3} - \frac{1249}{16}e$
41 $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ $-1$
43 $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ $-\frac{1}{8192}e^{15} + \frac{25}{2048}e^{13} - \frac{119}{256}e^{11} + \frac{4403}{512}e^{9} - \frac{2543}{32}e^{7} + \frac{10313}{32}e^{5} - \frac{1305}{4}e^{3} + 50e$
43 $[43, 43, w^{3} - w^{2} - 2w + 1]$ $-\frac{1}{4096}e^{15} + \frac{5}{256}e^{13} - \frac{5}{8}e^{11} + \frac{2579}{256}e^{9} - \frac{5353}{64}e^{7} + \frac{2525}{8}e^{5} - 330e^{3} + 67e$
64 $[64, 2, -2]$ $\phantom{-}\frac{15}{16384}e^{14} - \frac{225}{4096}e^{12} + \frac{1227}{1024}e^{10} - \frac{11153}{1024}e^{8} + \frac{3537}{128}e^{6} + \frac{1393}{16}e^{4} - \frac{1085}{8}e^{2} + \frac{85}{4}$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-\frac{11}{16384}e^{14} + \frac{175}{4096}e^{12} - \frac{1055}{1024}e^{10} + \frac{11789}{1024}e^{8} - \frac{1833}{32}e^{6} + \frac{3079}{32}e^{4} - \frac{215}{4}e^{2} + \frac{45}{4}$
71 $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ $\phantom{-}\frac{1}{8192}e^{14} - \frac{11}{2048}e^{12} + \frac{19}{512}e^{10} + \frac{737}{512}e^{8} - \frac{1743}{64}e^{6} + \frac{2395}{16}e^{4} - 166e^{2} + \frac{47}{2}$
83 $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ $\phantom{-}\frac{11}{32768}e^{15} - \frac{201}{8192}e^{13} + \frac{1463}{2048}e^{11} - \frac{21397}{2048}e^{9} + \frac{20155}{256}e^{7} - \frac{2175}{8}e^{5} + \frac{4387}{16}e^{3} - \frac{539}{8}e$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{8192}e^{15} - \frac{29}{4096}e^{13} + \frac{147}{1024}e^{11} - \frac{535}{512}e^{9} - \frac{271}{256}e^{7} + \frac{1163}{32}e^{5} - \frac{1005}{16}e^{3} + 26e$
83 $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ $-\frac{13}{8192}e^{14} + \frac{213}{2048}e^{12} - \frac{1343}{512}e^{10} + \frac{16171}{512}e^{8} - \frac{5803}{32}e^{6} + 428e^{4} - \frac{1331}{4}e^{2} + \frac{79}{2}$
83 $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ $\phantom{-}\frac{11}{16384}e^{14} - \frac{183}{4096}e^{12} + \frac{1179}{1024}e^{10} - \frac{14653}{1024}e^{8} + \frac{345}{4}e^{6} - \frac{6997}{32}e^{4} + \frac{651}{4}e^{2} - \frac{57}{4}$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ $-\frac{41}{65536}e^{15} + \frac{781}{16384}e^{13} - \frac{5945}{4096}e^{11} + \frac{91119}{4096}e^{9} - \frac{351}{2}e^{7} + \frac{80303}{128}e^{5} - \frac{9657}{16}e^{3} + \frac{1555}{16}e$
97 $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ $\phantom{-}\frac{33}{65536}e^{15} - \frac{657}{16384}e^{13} + \frac{5229}{4096}e^{11} - \frac{83735}{4096}e^{9} + \frac{43017}{256}e^{7} - \frac{79463}{128}e^{5} + \frac{2365}{4}e^{3} - \frac{1227}{16}e$
113 $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ $-\frac{9}{65536}e^{15} + \frac{121}{16384}e^{13} - \frac{517}{4096}e^{11} + \frac{1519}{4096}e^{9} + \frac{2431}{256}e^{7} - \frac{9769}{128}e^{5} + \frac{205}{2}e^{3} - \frac{301}{16}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ $1$