# Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 11 Level $[11, 11, -3w - 17]$ Label 2.2.157.1-11.1-a Dimension 13 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{157})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 39$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[11, 11, -3w - 17]$ Label 2.2.157.1-11.1-a Dimension 13 Is CM no Is base change no Parent newspace dimension 30

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{13}$$ $$\mathstrut -\mathstrut 16x^{11}$$ $$\mathstrut -\mathstrut 6x^{10}$$ $$\mathstrut +\mathstrut 90x^{9}$$ $$\mathstrut +\mathstrut 57x^{8}$$ $$\mathstrut -\mathstrut 209x^{7}$$ $$\mathstrut -\mathstrut 159x^{6}$$ $$\mathstrut +\mathstrut 201x^{5}$$ $$\mathstrut +\mathstrut 166x^{4}$$ $$\mathstrut -\mathstrut 58x^{3}$$ $$\mathstrut -\mathstrut 54x^{2}$$ $$\mathstrut -\mathstrut 5x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $-\frac{47}{53}e^{12} + \frac{26}{53}e^{11} + \frac{741}{53}e^{10} - \frac{111}{53}e^{9} - \frac{4234}{53}e^{8} - \frac{586}{53}e^{7} + \frac{10499}{53}e^{6} + \frac{2866}{53}e^{5} - \frac{11585}{53}e^{4} - \frac{3396}{53}e^{3} + \frac{4811}{53}e^{2} + \frac{949}{53}e - \frac{246}{53}$
3 $[3, 3, -w + 7]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}\frac{28}{53}e^{12} - \frac{20}{53}e^{11} - \frac{411}{53}e^{10} + \frac{118}{53}e^{9} + \frac{2095}{53}e^{8} + \frac{92}{53}e^{7} - \frac{4199}{53}e^{6} - \frac{1006}{53}e^{5} + \frac{3106}{53}e^{4} + \frac{1430}{53}e^{3} - \frac{480}{53}e^{2} - \frac{677}{53}e - \frac{35}{53}$
11 $[11, 11, -3w - 17]$ $\phantom{-}1$
11 $[11, 11, 3w - 20]$ $\phantom{-}\frac{93}{53}e^{12} - \frac{21}{53}e^{11} - \frac{1473}{53}e^{10} - \frac{210}{53}e^{9} + \frac{8255}{53}e^{8} + \frac{3160}{53}e^{7} - \frac{19347}{53}e^{6} - \frac{8895}{53}e^{5} + \frac{19421}{53}e^{4} + \frac{8312}{53}e^{3} - \frac{6758}{53}e^{2} - \frac{2065}{53}e + \frac{56}{53}$
13 $[13, 13, 2w - 13]$ $\phantom{-}\frac{34}{53}e^{12} + \frac{6}{53}e^{11} - \frac{571}{53}e^{10} - \frac{258}{53}e^{9} + \frac{3373}{53}e^{8} + \frac{2103}{53}e^{7} - \frac{8381}{53}e^{6} - \frac{5613}{53}e^{5} + \frac{8958}{53}e^{4} + \frac{5507}{53}e^{3} - \frac{3354}{53}e^{2} - \frac{1265}{53}e + \frac{37}{53}$
13 $[13, 13, 2w + 11]$ $-\frac{34}{53}e^{12} - \frac{6}{53}e^{11} + \frac{571}{53}e^{10} + \frac{258}{53}e^{9} - \frac{3373}{53}e^{8} - \frac{2103}{53}e^{7} + \frac{8381}{53}e^{6} + \frac{5613}{53}e^{5} - \frac{8958}{53}e^{4} - \frac{5560}{53}e^{3} + \frac{3460}{53}e^{2} + \frac{1530}{53}e - \frac{249}{53}$
17 $[17, 17, w + 7]$ $\phantom{-}\frac{3}{53}e^{12} + \frac{66}{53}e^{11} - \frac{133}{53}e^{10} - \frac{930}{53}e^{9} + \frac{1063}{53}e^{8} + \frac{4583}{53}e^{7} - \frac{2992}{53}e^{6} - \frac{8849}{53}e^{5} + \frac{3880}{53}e^{4} + \frac{6093}{53}e^{3} - \frac{2285}{53}e^{2} - \frac{665}{53}e + \frac{301}{53}$
17 $[17, 17, -w + 8]$ $-\frac{91}{53}e^{12} + \frac{12}{53}e^{11} + \frac{1455}{53}e^{10} + \frac{332}{53}e^{9} - \frac{8253}{53}e^{8} - \frac{3744}{53}e^{7} + \frac{19755}{53}e^{6} + \frac{10080}{53}e^{5} - \frac{20827}{53}e^{4} - \frac{9285}{53}e^{3} + \frac{8344}{53}e^{2} + \frac{2134}{53}e - \frac{562}{53}$
19 $[19, 19, -w - 4]$ $...$
19 $[19, 19, -w + 5]$ $-\frac{168}{53}e^{12} + \frac{67}{53}e^{11} + \frac{2625}{53}e^{10} - \frac{19}{53}e^{9} - \frac{14584}{53}e^{8} - \frac{3838}{53}e^{7} + \frac{34045}{53}e^{6} + \frac{12767}{53}e^{5} - \frac{34059}{53}e^{4} - \frac{13138}{53}e^{3} + \frac{11678}{53}e^{2} + \frac{3532}{53}e - \frac{55}{53}$
25 $[25, 5, 5]$ $...$
31 $[31, 31, -6w - 35]$ $\phantom{-}\frac{5}{53}e^{12} + \frac{57}{53}e^{11} - \frac{151}{53}e^{10} - \frac{861}{53}e^{9} + \frac{1171}{53}e^{8} + \frac{4635}{53}e^{7} - \frac{3538}{53}e^{6} - \frac{10473}{53}e^{5} + \frac{5071}{53}e^{4} + \frac{10155}{53}e^{3} - \frac{2819}{53}e^{2} - \frac{3246}{53}e - \frac{99}{53}$
31 $[31, 31, -6w + 41]$ $-\frac{84}{53}e^{12} + \frac{60}{53}e^{11} + \frac{1286}{53}e^{10} - \frac{354}{53}e^{9} - \frac{7080}{53}e^{8} - \frac{541}{53}e^{7} + \frac{16519}{53}e^{6} + \frac{5085}{53}e^{5} - \frac{16102}{53}e^{4} - \frac{7682}{53}e^{3} + \frac{4885}{53}e^{2} + \frac{2985}{53}e - \frac{1}{53}$
37 $[37, 37, -w - 1]$ $...$
37 $[37, 37, w - 2]$ $-\frac{119}{53}e^{12} + \frac{85}{53}e^{11} + \frac{1760}{53}e^{10} - \frac{528}{53}e^{9} - \frac{9129}{53}e^{8} + \frac{33}{53}e^{7} + \frac{19078}{53}e^{6} + \frac{2235}{53}e^{5} - \frac{15824}{53}e^{4} - \frac{2606}{53}e^{3} + \frac{3842}{53}e^{2} + \frac{1009}{53}e + \frac{3}{53}$
47 $[47, 47, 3w + 16]$ $-\frac{71}{53}e^{12} + \frac{28}{53}e^{11} + \frac{1063}{53}e^{10} + \frac{15}{53}e^{9} - \frac{5477}{53}e^{8} - \frac{1687}{53}e^{7} + \frac{11009}{53}e^{6} + \frac{4970}{53}e^{5} - \frac{8334}{53}e^{4} - \frac{4970}{53}e^{3} + \frac{1202}{53}e^{2} + \frac{1923}{53}e + \frac{367}{53}$
47 $[47, 47, -3w + 19]$ $-\frac{142}{53}e^{12} + \frac{56}{53}e^{11} + \frac{2232}{53}e^{10} + \frac{30}{53}e^{9} - \frac{12597}{53}e^{8} - \frac{3745}{53}e^{7} + \frac{30339}{53}e^{6} + \frac{12802}{53}e^{5} - \frac{32038}{53}e^{4} - \frac{13756}{53}e^{3} + \frac{12792}{53}e^{2} + \frac{3846}{53}e - \frac{697}{53}$
49 $[49, 7, -7]$ $-\frac{325}{53}e^{12} + \frac{111}{53}e^{11} + \frac{5151}{53}e^{10} + \frac{156}{53}e^{9} - \frac{29051}{53}e^{8} - \frac{8185}{53}e^{7} + \frac{69115}{53}e^{6} + \frac{26354}{53}e^{5} - \frac{70657}{53}e^{4} - \frac{27520}{53}e^{3} + \frac{25136}{53}e^{2} + \frac{8106}{53}e - \frac{561}{53}$
67 $[67, 67, 3w - 22]$ $-\frac{302}{53}e^{12} + \frac{140}{53}e^{11} + \frac{4732}{53}e^{10} - \frac{349}{53}e^{9} - \frac{26537}{53}e^{8} - \frac{5202}{53}e^{7} + \frac{63366}{53}e^{6} + \frac{19550}{53}e^{5} - \frac{66262}{53}e^{4} - \frac{21405}{53}e^{3} + \frac{24931}{53}e^{2} + \frac{6382}{53}e - \frac{497}{53}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -3w - 17]$ $-1$