Properties

Label 2.2.481.1-4.1-m
Base field \(\Q(\sqrt{481}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $16$
CM no
Base change no

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Base field \(\Q(\sqrt{481}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 120\); narrow class number \(2\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[4, 2, 2]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $80$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} + 45x^{14} + 732x^{12} + 5418x^{10} + 19458x^{8} + 34533x^{6} + 28728x^{4} + 8748x^{2} + 81\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-\frac{2279}{49248}e^{15} - \frac{2747}{1368}e^{13} - \frac{62879}{2052}e^{11} - \frac{550783}{2736}e^{9} - \frac{98225}{171}e^{7} - \frac{1201609}{1824}e^{5} - \frac{137197}{608}e^{3} + \frac{4945}{608}e$
2 $[2, 2, w + 1]$ $-\frac{2279}{49248}e^{15} - \frac{2747}{1368}e^{13} - \frac{62879}{2052}e^{11} - \frac{550783}{2736}e^{9} - \frac{98225}{171}e^{7} - \frac{1201609}{1824}e^{5} - \frac{137197}{608}e^{3} + \frac{4945}{608}e$
3 $[3, 3, -2w - 21]$ $-\frac{13657}{377568}e^{14} - \frac{296489}{188784}e^{12} - \frac{1509887}{62928}e^{10} - \frac{2485841}{15732}e^{8} - \frac{3170797}{6992}e^{6} - \frac{321491}{608}e^{4} - \frac{2733221}{13984}e^{2} - \frac{40277}{13984}$
3 $[3, 3, 2w - 23]$ $-\frac{74269}{377568}e^{14} - \frac{1613401}{188784}e^{12} - \frac{2741981}{20976}e^{10} - \frac{6787079}{7866}e^{8} - \frac{52197647}{20976}e^{6} - \frac{1782823}{608}e^{4} - \frac{15429033}{13984}e^{2} - \frac{120753}{13984}$
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, w + 4]$ $-\frac{3241}{20976}e^{15} - \frac{634321}{94392}e^{13} - \frac{1080101}{10488}e^{11} - \frac{5367923}{7866}e^{9} - \frac{20825023}{10488}e^{7} - \frac{2183105}{912}e^{5} - \frac{6836205}{6992}e^{3} - \frac{369629}{6992}e$
13 $[13, 13, w + 6]$ $\phantom{-}\frac{2639}{23598}e^{15} + \frac{457933}{94392}e^{13} + \frac{776099}{10488}e^{11} + \frac{5094361}{10488}e^{9} + \frac{14513485}{10488}e^{7} + \frac{721781}{456}e^{5} + \frac{943687}{1748}e^{3} - \frac{74809}{3496}e$
19 $[19, 19, w + 2]$ $\phantom{-}\frac{23515}{94392}e^{15} + \frac{28387}{2622}e^{13} + \frac{217195}{1311}e^{11} + \frac{17217917}{15732}e^{9} + \frac{4144615}{1311}e^{7} + \frac{567763}{152}e^{5} + \frac{4925803}{3496}e^{3} + \frac{22657}{3496}e$
19 $[19, 19, w + 16]$ $-\frac{555}{6992}e^{15} - \frac{324397}{94392}e^{13} - \frac{547777}{10488}e^{11} - \frac{446057}{1311}e^{9} - \frac{9986243}{10488}e^{7} - \frac{945233}{912}e^{5} - \frac{1972069}{6992}e^{3} + \frac{360691}{6992}e$
31 $[31, 31, w + 13]$ $-\frac{9187}{377568}e^{15} - \frac{100261}{94392}e^{13} - \frac{21476}{1311}e^{11} - \frac{6909077}{62928}e^{9} - \frac{1708357}{5244}e^{7} - \frac{731465}{1824}e^{5} - \frac{2102467}{13984}e^{3} + \frac{158823}{13984}e$
31 $[31, 31, w + 17]$ $-\frac{86765}{377568}e^{15} - \frac{314011}{31464}e^{13} - \frac{799877}{5244}e^{11} - \frac{21086117}{20976}e^{9} - \frac{7575391}{2622}e^{7} - \frac{6155743}{1824}e^{5} - \frac{17169853}{13984}e^{3} + \frac{266177}{13984}e$
37 $[37, 37, w + 18]$ $-\frac{5725}{31464}e^{15} - \frac{27685}{3496}e^{13} - \frac{424807}{3496}e^{11} - \frac{25401527}{31464}e^{9} - \frac{24790907}{10488}e^{7} - \frac{330551}{114}e^{5} - \frac{4427165}{3496}e^{3} - \frac{207881}{1748}e$
49 $[49, 7, -7]$ $-\frac{59117}{377568}e^{14} - \frac{428245}{62928}e^{12} - \frac{6554573}{62928}e^{10} - \frac{2406481}{3496}e^{8} - \frac{41734045}{20976}e^{6} - \frac{1430507}{608}e^{4} - \frac{12439937}{13984}e^{2} - \frac{97381}{13984}$
53 $[53, 53, -234w + 2683]$ $-\frac{32759}{41952}e^{14} - \frac{800519}{23598}e^{12} - \frac{16322639}{31464}e^{10} - \frac{215396371}{62928}e^{8} - \frac{34482567}{3496}e^{6} - \frac{7053443}{608}e^{4} - \frac{60820359}{13984}e^{2} - \frac{537041}{13984}$
53 $[53, 53, -234w - 2449]$ $\phantom{-}\frac{61361}{377568}e^{14} + \frac{667031}{94392}e^{12} + \frac{141898}{1311}e^{10} + \frac{45069703}{62928}e^{8} + \frac{3626945}{1748}e^{6} + \frac{1497201}{608}e^{4} + \frac{13051217}{13984}e^{2} + \frac{87683}{13984}$
59 $[59, 59, w + 1]$ $-\frac{12391}{125856}e^{15} - \frac{809765}{188784}e^{13} - \frac{4150091}{62928}e^{11} - \frac{6923597}{15732}e^{9} - \frac{27326387}{20976}e^{7} - \frac{1001831}{608}e^{5} - \frac{11070689}{13984}e^{3} - \frac{1479057}{13984}e$
59 $[59, 59, w + 57]$ $-\frac{90979}{377568}e^{15} - \frac{1974253}{188784}e^{13} - \frac{10045247}{62928}e^{11} - \frac{3667953}{3496}e^{9} - \frac{62829247}{20976}e^{7} - \frac{6256039}{1824}e^{5} - \frac{15953183}{13984}e^{3} + \frac{1181581}{13984}e$
89 $[89, 89, w + 41]$ $-\frac{89387}{188784}e^{15} - \frac{80797}{3933}e^{13} - \frac{4930799}{15732}e^{11} - \frac{64761631}{31464}e^{9} - \frac{10259735}{1748}e^{7} - \frac{6136781}{912}e^{5} - \frac{16218067}{6992}e^{3} + \frac{441851}{6992}e$
89 $[89, 89, w + 47]$ $\phantom{-}\frac{74753}{188784}e^{15} + \frac{45077}{2622}e^{13} + \frac{4131571}{15732}e^{11} + \frac{54403457}{31464}e^{9} + \frac{8668343}{1748}e^{7} + \frac{5257855}{912}e^{5} + \frac{14470537}{6992}e^{3} - \frac{271177}{6992}e$
97 $[97, 97, w + 26]$ $\phantom{-}\frac{20413}{41952}e^{15} + \frac{998723}{47196}e^{13} + \frac{10201783}{31464}e^{11} + \frac{135138157}{62928}e^{9} + \frac{21810123}{3496}e^{7} + \frac{4544185}{608}e^{5} + \frac{41307613}{13984}e^{3} + \frac{1238643}{13984}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $\frac{2279}{49248}e^{15} + \frac{2747}{1368}e^{13} + \frac{62879}{2052}e^{11} + \frac{550783}{2736}e^{9} + \frac{98225}{171}e^{7} + \frac{1201609}{1824}e^{5} + \frac{137197}{608}e^{3} - \frac{4945}{608}e$
$2$ $[2, 2, w + 1]$ $\frac{2279}{49248}e^{15} + \frac{2747}{1368}e^{13} + \frac{62879}{2052}e^{11} + \frac{550783}{2736}e^{9} + \frac{98225}{171}e^{7} + \frac{1201609}{1824}e^{5} + \frac{137197}{608}e^{3} - \frac{4945}{608}e$