# Properties

 Label 4.4.16317.1-25.1-i Base field 4.4.16317.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, w^{2} - w - 3]$ Dimension $12$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.16317.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, w^{2} - w - 3]$ Dimension: $12$ CM: no Base change: yes Newspace dimension: $50$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{12} - 39x^{10} + 540x^{8} - 3217x^{6} + 8303x^{4} - 7948x^{2} + 2476$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-\frac{4679}{189463}e^{10} + \frac{180218}{189463}e^{8} - \frac{2436906}{189463}e^{6} + \frac{13741647}{189463}e^{4} - \frac{30428771}{189463}e^{2} + \frac{16152958}{189463}$
7 $[7, 7, -w^{2} + 2]$ $-\frac{4679}{189463}e^{10} + \frac{180218}{189463}e^{8} - \frac{2436906}{189463}e^{6} + \frac{13741647}{189463}e^{4} - \frac{30428771}{189463}e^{2} + \frac{16152958}{189463}$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $\phantom{-}\frac{1585}{189463}e^{10} - \frac{60603}{189463}e^{8} + \frac{820556}{189463}e^{6} - \frac{4714028}{189463}e^{4} + \frac{10852779}{189463}e^{2} - \frac{5480522}{189463}$
16 $[16, 2, 2]$ $-\frac{1509}{378926}e^{10} + \frac{29506}{189463}e^{8} - \frac{397897}{189463}e^{6} + \frac{4313591}{378926}e^{4} - \frac{4266875}{189463}e^{2} + \frac{2217031}{189463}$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{301}{189463}e^{11} - \frac{13780}{189463}e^{9} + \frac{232689}{189463}e^{7} - \frac{1747982}{189463}e^{5} + \frac{5447667}{189463}e^{3} - \frac{4802667}{189463}e$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{301}{189463}e^{11} - \frac{13780}{189463}e^{9} + \frac{232689}{189463}e^{7} - \frac{1747982}{189463}e^{5} + \frac{5447667}{189463}e^{3} - \frac{4802667}{189463}e$
25 $[25, 5, w^{2} - w - 3]$ $-1$
37 $[37, 37, 2w - 1]$ $\phantom{-}\frac{4077}{189463}e^{10} - \frac{152658}{189463}e^{8} + \frac{1971528}{189463}e^{6} - \frac{10245683}{189463}e^{4} + \frac{19722900}{189463}e^{2} - \frac{8442254}{189463}$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $-\frac{3175}{378926}e^{10} + \frac{54423}{189463}e^{8} - \frac{614457}{189463}e^{6} + \frac{5079301}{378926}e^{4} - \frac{3401648}{189463}e^{2} + \frac{1461434}{189463}$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $-\frac{3175}{378926}e^{10} + \frac{54423}{189463}e^{8} - \frac{614457}{189463}e^{6} + \frac{5079301}{378926}e^{4} - \frac{3401648}{189463}e^{2} + \frac{1461434}{189463}$
59 $[59, 59, 2w - 5]$ $-\frac{7397}{378926}e^{11} + \frac{140995}{189463}e^{9} - \frac{1875629}{189463}e^{7} + \frac{20698411}{378926}e^{5} - \frac{22830732}{189463}e^{3} + \frac{13606200}{189463}e$
59 $[59, 59, -2w - 3]$ $-\frac{7397}{378926}e^{11} + \frac{140995}{189463}e^{9} - \frac{1875629}{189463}e^{7} + \frac{20698411}{378926}e^{5} - \frac{22830732}{189463}e^{3} + \frac{13606200}{189463}e$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $-\frac{11921}{378926}e^{10} + \frac{233221}{189463}e^{8} - \frac{3230872}{189463}e^{6} + \frac{37764141}{378926}e^{4} - \frac{43474477}{189463}e^{2} + \frac{23312920}{189463}$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $-\frac{11921}{378926}e^{10} + \frac{233221}{189463}e^{8} - \frac{3230872}{189463}e^{6} + \frac{37764141}{378926}e^{4} - \frac{43474477}{189463}e^{2} + \frac{23312920}{189463}$
83 $[83, 83, -w^{3} + 7w]$ $-\frac{32301}{378926}e^{11} + \frac{621046}{189463}e^{9} - \frac{8365791}{189463}e^{7} + \frac{93720237}{378926}e^{5} - \frac{103074803}{189463}e^{3} + \frac{53932070}{189463}e$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}\frac{6038}{189463}e^{11} - \frac{231104}{189463}e^{9} + \frac{3094082}{189463}e^{7} - \frac{17220029}{189463}e^{5} + \frac{38139849}{189463}e^{3} - \frac{22251068}{189463}e$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{6038}{189463}e^{11} - \frac{231104}{189463}e^{9} + \frac{3094082}{189463}e^{7} - \frac{17220029}{189463}e^{5} + \frac{38139849}{189463}e^{3} - \frac{22251068}{189463}e$
83 $[83, 83, w^{2} - 2w - 6]$ $-\frac{32301}{378926}e^{11} + \frac{621046}{189463}e^{9} - \frac{8365791}{189463}e^{7} + \frac{93720237}{378926}e^{5} - \frac{103074803}{189463}e^{3} + \frac{53932070}{189463}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{2} - w - 3]$ $1$