Properties

Base field \(\Q(\sqrt{197}) \)
Weight [2, 2]
Level norm 25
Level $[25, 5, 5]$
Label 2.2.197.1-25.1-c
Dimension 44
CM no
Base change no

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Base field \(\Q(\sqrt{197}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[25, 5, 5]$
Label 2.2.197.1-25.1-c
Dimension 44
Is CM no
Is base change no
Parent newspace dimension 99

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{44} \) \(\mathstrut +\mathstrut 13x^{43} \) \(\mathstrut -\mathstrut 94x^{42} \) \(\mathstrut -\mathstrut 1851x^{41} \) \(\mathstrut +\mathstrut 1958x^{40} \) \(\mathstrut +\mathstrut 117785x^{39} \) \(\mathstrut +\mathstrut 126578x^{38} \) \(\mathstrut -\mathstrut 4445808x^{37} \) \(\mathstrut -\mathstrut 9868994x^{36} \) \(\mathstrut +\mathstrut 111519135x^{35} \) \(\mathstrut +\mathstrut 333474226x^{34} \) \(\mathstrut -\mathstrut 1976448483x^{33} \) \(\mathstrut -\mathstrut 7090755347x^{32} \) \(\mathstrut +\mathstrut 25728697545x^{31} \) \(\mathstrut +\mathstrut 105173010312x^{30} \) \(\mathstrut -\mathstrut 252964633239x^{29} \) \(\mathstrut -\mathstrut 1139807586785x^{28} \) \(\mathstrut +\mathstrut 1920691723498x^{27} \) \(\mathstrut +\mathstrut 9243276535070x^{26} \) \(\mathstrut -\mathstrut 11470367212338x^{25} \) \(\mathstrut -\mathstrut 56722187434068x^{24} \) \(\mathstrut +\mathstrut 54583745724477x^{23} \) \(\mathstrut +\mathstrut 263975522112466x^{22} \) \(\mathstrut -\mathstrut 207590654932305x^{21} \) \(\mathstrut -\mathstrut 926693951326708x^{20} \) \(\mathstrut +\mathstrut 623013118092945x^{19} \) \(\mathstrut +\mathstrut 2424329500591734x^{18} \) \(\mathstrut -\mathstrut 1430157291894188x^{17} \) \(\mathstrut -\mathstrut 4640473489510500x^{16} \) \(\mathstrut +\mathstrut 2391829221943340x^{15} \) \(\mathstrut +\mathstrut 6346404211836478x^{14} \) \(\mathstrut -\mathstrut 2730269456307623x^{13} \) \(\mathstrut -\mathstrut 6025048407925914x^{12} \) \(\mathstrut +\mathstrut 1947561184009861x^{11} \) \(\mathstrut +\mathstrut 3828908929741662x^{10} \) \(\mathstrut -\mathstrut 753603997378366x^{9} \) \(\mathstrut -\mathstrut 1543962178555169x^{8} \) \(\mathstrut +\mathstrut 108027900960064x^{7} \) \(\mathstrut +\mathstrut 361494068458152x^{6} \) \(\mathstrut +\mathstrut 12278026643680x^{5} \) \(\mathstrut -\mathstrut 42375208908272x^{4} \) \(\mathstrut -\mathstrut 4071883492864x^{3} \) \(\mathstrut +\mathstrut 2006242069632x^{2} \) \(\mathstrut +\mathstrut 241022914048x \) \(\mathstrut -\mathstrut 14666340608\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $...$
7 $[7, 7, w - 7]$ $...$
7 $[7, 7, w + 6]$ $\phantom{-}e$
9 $[9, 3, 3]$ $...$
19 $[19, 19, w + 5]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 8]$ $...$
23 $[23, 23, -w + 9]$ $...$
25 $[25, 5, 5]$ $\phantom{-}1$
29 $[29, 29, -w - 4]$ $...$
29 $[29, 29, w - 5]$ $...$
37 $[37, 37, -w - 3]$ $...$
37 $[37, 37, w - 4]$ $...$
41 $[41, 41, -w - 9]$ $...$
41 $[41, 41, w - 10]$ $...$
43 $[43, 43, -w - 2]$ $...$
43 $[43, 43, w - 3]$ $...$
47 $[47, 47, -w - 1]$ $...$
47 $[47, 47, w - 2]$ $...$
53 $[53, 53, 2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25, 5, 5]$ $-1$