Properties

Label 4.4.11525.1-16.1-d
Base field 4.4.11525.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $11$
CM no
Base change yes

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Base field 4.4.11525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $11$
CM: no
Base change: yes
Newspace dimension: $17$

Hecke eigenvalues ($q$-expansion)

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

\(x^{11} - 3x^{10} - 28x^{9} + 77x^{8} + 246x^{7} - 587x^{6} - 764x^{5} + 1151x^{4} + 1359x^{3} - 364x^{2} - 736x - 192\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{17540}{49759}e^{10} - \frac{264347}{199036}e^{9} - \frac{1757827}{199036}e^{8} + \frac{99176}{2927}e^{7} + \frac{11980401}{199036}e^{6} - \frac{25091513}{99518}e^{5} - \frac{14313187}{199036}e^{4} + \frac{22592735}{49759}e^{3} + \frac{24903875}{199036}e^{2} - \frac{43289233}{199036}e - \frac{4450014}{49759}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}\frac{17540}{49759}e^{10} - \frac{264347}{199036}e^{9} - \frac{1757827}{199036}e^{8} + \frac{99176}{2927}e^{7} + \frac{11980401}{199036}e^{6} - \frac{25091513}{99518}e^{5} - \frac{14313187}{199036}e^{4} + \frac{22592735}{49759}e^{3} + \frac{24903875}{199036}e^{2} - \frac{43289233}{199036}e - \frac{4450014}{49759}$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}\frac{184289}{796144}e^{10} - \frac{720943}{796144}e^{9} - \frac{561245}{99518}e^{8} + \frac{1075661}{46832}e^{7} + \frac{14137797}{398072}e^{6} - \frac{134196867}{796144}e^{5} - \frac{1798733}{99518}e^{4} + \frac{228517839}{796144}e^{3} + \frac{25186459}{796144}e^{2} - \frac{6301777}{49759}e - \frac{1709944}{49759}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-\frac{329479}{796144}e^{10} + \frac{1202149}{796144}e^{9} + \frac{2110725}{199036}e^{8} - \frac{1814923}{46832}e^{7} - \frac{30453349}{398072}e^{6} + \frac{233006461}{796144}e^{5} + \frac{24728329}{199036}e^{4} - \frac{443681033}{796144}e^{3} - \frac{153596745}{796144}e^{2} + \frac{55610965}{199036}e + \frac{5858451}{49759}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{184289}{796144}e^{10} - \frac{720943}{796144}e^{9} - \frac{561245}{99518}e^{8} + \frac{1075661}{46832}e^{7} + \frac{14137797}{398072}e^{6} - \frac{134196867}{796144}e^{5} - \frac{1798733}{99518}e^{4} + \frac{228517839}{796144}e^{3} + \frac{25186459}{796144}e^{2} - \frac{6301777}{49759}e - \frac{1709944}{49759}$
19 $[19, 19, w - 1]$ $-\frac{329479}{796144}e^{10} + \frac{1202149}{796144}e^{9} + \frac{2110725}{199036}e^{8} - \frac{1814923}{46832}e^{7} - \frac{30453349}{398072}e^{6} + \frac{233006461}{796144}e^{5} + \frac{24728329}{199036}e^{4} - \frac{443681033}{796144}e^{3} - \frac{153596745}{796144}e^{2} + \frac{55610965}{199036}e + \frac{5858451}{49759}$
29 $[29, 29, w^{2} - w - 8]$ $-\frac{1544}{49759}e^{10} + \frac{6937}{99518}e^{9} + \frac{100699}{99518}e^{8} - \frac{5908}{2927}e^{7} - \frac{1112245}{99518}e^{6} + \frac{963422}{49759}e^{5} + \frac{4789715}{99518}e^{4} - \frac{3229066}{49759}e^{3} - \frac{7269745}{99518}e^{2} + \frac{4365399}{99518}e + \frac{1772992}{49759}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $-\frac{1544}{49759}e^{10} + \frac{6937}{99518}e^{9} + \frac{100699}{99518}e^{8} - \frac{5908}{2927}e^{7} - \frac{1112245}{99518}e^{6} + \frac{963422}{49759}e^{5} + \frac{4789715}{99518}e^{4} - \frac{3229066}{49759}e^{3} - \frac{7269745}{99518}e^{2} + \frac{4365399}{99518}e + \frac{1772992}{49759}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $\phantom{-}\frac{156215}{398072}e^{10} - \frac{555877}{398072}e^{9} - \frac{1018475}{99518}e^{8} + \frac{841467}{23416}e^{7} + \frac{15377953}{199036}e^{6} - \frac{108901565}{398072}e^{5} - \frac{15308425}{99518}e^{4} + \frac{213945889}{398072}e^{3} + \frac{98081137}{398072}e^{2} - \frac{27013701}{99518}e - \frac{6831340}{49759}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{156215}{398072}e^{10} - \frac{555877}{398072}e^{9} - \frac{1018475}{99518}e^{8} + \frac{841467}{23416}e^{7} + \frac{15377953}{199036}e^{6} - \frac{108901565}{398072}e^{5} - \frac{15308425}{99518}e^{4} + \frac{213945889}{398072}e^{3} + \frac{98081137}{398072}e^{2} - \frac{27013701}{99518}e - \frac{6831340}{49759}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-\frac{193791}{99518}e^{10} + \frac{354370}{49759}e^{9} + \frac{4953897}{99518}e^{8} - \frac{1068509}{5854}e^{7} - \frac{35554085}{99518}e^{6} + \frac{136824409}{99518}e^{5} + \frac{56647373}{99518}e^{4} - \frac{258494795}{99518}e^{3} - \frac{45168291}{49759}e^{2} + \frac{128854165}{99518}e + \frac{28442946}{49759}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $-\frac{193791}{99518}e^{10} + \frac{354370}{49759}e^{9} + \frac{4953897}{99518}e^{8} - \frac{1068509}{5854}e^{7} - \frac{35554085}{99518}e^{6} + \frac{136824409}{99518}e^{5} + \frac{56647373}{99518}e^{4} - \frac{258494795}{99518}e^{3} - \frac{45168291}{49759}e^{2} + \frac{128854165}{99518}e + \frac{28442946}{49759}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}\frac{189133}{199036}e^{10} - \frac{722221}{199036}e^{9} - \frac{2361119}{99518}e^{8} + \frac{1086037}{11708}e^{7} + \frac{7975583}{49759}e^{6} - \frac{137883815}{199036}e^{5} - \frac{17820211}{99518}e^{4} + \frac{251246199}{199036}e^{3} + \frac{60408677}{199036}e^{2} - \frac{60446167}{99518}e - \frac{11253562}{49759}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}\frac{189133}{199036}e^{10} - \frac{722221}{199036}e^{9} - \frac{2361119}{99518}e^{8} + \frac{1086037}{11708}e^{7} + \frac{7975583}{49759}e^{6} - \frac{137883815}{199036}e^{5} - \frac{17820211}{99518}e^{4} + \frac{251246199}{199036}e^{3} + \frac{60408677}{199036}e^{2} - \frac{60446167}{99518}e - \frac{11253562}{49759}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{164341}{199036}e^{10} - \frac{594467}{199036}e^{9} - \frac{1056402}{49759}e^{8} + \frac{896477}{11708}e^{7} + \frac{15395191}{99518}e^{6} - \frac{114984335}{199036}e^{5} - \frac{13218598}{49759}e^{4} + \frac{218919647}{199036}e^{3} + \frac{85135535}{199036}e^{2} - \frac{27534071}{49759}e - \frac{12955276}{49759}$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}\frac{164341}{199036}e^{10} - \frac{594467}{199036}e^{9} - \frac{1056402}{49759}e^{8} + \frac{896477}{11708}e^{7} + \frac{15395191}{99518}e^{6} - \frac{114984335}{199036}e^{5} - \frac{13218598}{49759}e^{4} + \frac{218919647}{199036}e^{3} + \frac{85135535}{199036}e^{2} - \frac{27534071}{49759}e - \frac{12955276}{49759}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{138245}{99518}e^{10} - \frac{508773}{99518}e^{9} - \frac{1760661}{49759}e^{8} + \frac{766473}{5854}e^{7} + \frac{12526165}{49759}e^{6} - \frac{97945597}{99518}e^{5} - \frac{19125945}{49759}e^{4} + \frac{183421477}{99518}e^{3} + \frac{61339227}{99518}e^{2} - \frac{44679081}{49759}e - \frac{19292060}{49759}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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