Properties

Label 4.4.11661.1-16.1-d
Base field 4.4.11661.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $12$
CM no
Base change yes

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Base field 4.4.11661.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $12$
CM: no
Base change: yes
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 34x^{10} + 431x^{8} - 2532x^{6} + 6946x^{4} - 7344x^{2} + 800\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-\frac{259}{43520}e^{11} + \frac{3913}{21760}e^{9} - \frac{81429}{43520}e^{7} + \frac{10479}{1360}e^{5} - \frac{223347}{21760}e^{3} - \frac{5123}{5440}e$
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-\frac{259}{43520}e^{11} + \frac{3913}{21760}e^{9} - \frac{81429}{43520}e^{7} + \frac{10479}{1360}e^{5} - \frac{223347}{21760}e^{3} - \frac{5123}{5440}e$
16 $[16, 2, 2]$ $-1$
23 $[23, 23, -w^{3} + 4w + 1]$ $-\frac{7}{136}e^{10} + \frac{103}{68}e^{8} - \frac{2085}{136}e^{6} + \frac{1052}{17}e^{4} - \frac{5939}{68}e^{2} + \frac{321}{17}$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{473}{43520}e^{11} - \frac{6411}{21760}e^{9} + \frac{110063}{43520}e^{7} - \frac{8873}{1360}e^{5} - \frac{68311}{21760}e^{3} + \frac{77881}{5440}e$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}\frac{473}{43520}e^{11} - \frac{6411}{21760}e^{9} + \frac{110063}{43520}e^{7} - \frac{8873}{1360}e^{5} - \frac{68311}{21760}e^{3} + \frac{77881}{5440}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $-\frac{11}{4352}e^{11} + \frac{225}{2176}e^{9} - \frac{6861}{4352}e^{7} + \frac{1443}{136}e^{5} - \frac{61819}{2176}e^{3} + \frac{11093}{544}e$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $-\frac{11}{4352}e^{11} + \frac{225}{2176}e^{9} - \frac{6861}{4352}e^{7} + \frac{1443}{136}e^{5} - \frac{61819}{2176}e^{3} + \frac{11093}{544}e$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{63}{4352}e^{10} + \frac{893}{2176}e^{8} - \frac{17337}{4352}e^{6} + \frac{2163}{136}e^{4} - \frac{59503}{2176}e^{2} + \frac{8193}{544}$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $-\frac{63}{4352}e^{10} + \frac{893}{2176}e^{8} - \frac{17337}{4352}e^{6} + \frac{2163}{136}e^{4} - \frac{59503}{2176}e^{2} + \frac{8193}{544}$
61 $[61, 61, -w^{2} + 2w + 4]$ $\phantom{-}\frac{39}{4352}e^{11} - \frac{501}{2176}e^{9} + \frac{7313}{4352}e^{7} - \frac{115}{136}e^{5} - \frac{51241}{2176}e^{3} + \frac{24071}{544}e$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}\frac{39}{4352}e^{11} - \frac{501}{2176}e^{9} + \frac{7313}{4352}e^{7} - \frac{115}{136}e^{5} - \frac{51241}{2176}e^{3} + \frac{24071}{544}e$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}\frac{601}{21760}e^{11} - \frac{9227}{10880}e^{9} + \frac{199791}{21760}e^{7} - \frac{28681}{680}e^{5} + \frac{879913}{10880}e^{3} - \frac{133543}{2720}e$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}\frac{601}{21760}e^{11} - \frac{9227}{10880}e^{9} + \frac{199791}{21760}e^{7} - \frac{28681}{680}e^{5} + \frac{879913}{10880}e^{3} - \frac{133543}{2720}e$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $-\frac{37}{1280}e^{11} + \frac{559}{640}e^{9} - \frac{11907}{1280}e^{7} + \frac{1677}{40}e^{5} - \frac{50101}{640}e^{3} + \frac{8731}{160}e$
101 $[101, 101, w^{3} - 4w - 4]$ $-\frac{37}{1280}e^{11} + \frac{559}{640}e^{9} - \frac{11907}{1280}e^{7} + \frac{1677}{40}e^{5} - \frac{50101}{640}e^{3} + \frac{8731}{160}e$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $-\frac{137}{1088}e^{10} + \frac{2011}{544}e^{8} - \frac{40447}{1088}e^{6} + \frac{5021}{34}e^{4} - \frac{107385}{544}e^{2} + \frac{1911}{136}$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $-\frac{137}{1088}e^{10} + \frac{2011}{544}e^{8} - \frac{40447}{1088}e^{6} + \frac{5021}{34}e^{4} - \frac{107385}{544}e^{2} + \frac{1911}{136}$
107 $[107, 107, 2w^{2} - 3w - 4]$ $\phantom{-}\frac{263}{4352}e^{10} - \frac{3797}{2176}e^{8} + \frac{74033}{4352}e^{6} - \frac{8667}{136}e^{4} + \frac{173623}{2176}e^{2} - \frac{10681}{544}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$