Properties

Label 722.2.c.m
Level $722$
Weight $2$
Character orbit 722.c
Analytic conductor $5.765$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.324000000.2
Defining polynomial: \( x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{7}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + ( - \beta_{4} - 1) q^{2} + (\beta_{6} + \beta_{3}) q^{3} + \beta_{4} q^{4} + ( - \beta_{6} + \beta_{3} - \beta_1) q^{5} + (\beta_{7} - \beta_{6} - \beta_{2}) q^{6} + ( - \beta_{5} + \beta_{2} - 1) q^{7} + q^{8} + ( - 2 \beta_{5} + \beta_{4} - 2 \beta_1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + ( - \beta_{4} - 1) q^{2} + (\beta_{6} + \beta_{3}) q^{3} + \beta_{4} q^{4} + ( - \beta_{6} + \beta_{3} - \beta_1) q^{5} + (\beta_{7} - \beta_{6} - \beta_{2}) q^{6} + ( - \beta_{5} + \beta_{2} - 1) q^{7} + q^{8} + ( - 2 \beta_{5} + \beta_{4} - 2 \beta_1) q^{9} + (\beta_{7} + \beta_{6} + \beta_{5} + \beta_{2} + \beta_1) q^{10} + (\beta_{5} + 3 \beta_{2} - 1) q^{11} + ( - \beta_{7} - \beta_{3} + \beta_{2}) q^{12} + ( - \beta_{7} + \beta_{6} + \beta_{5} + 5 \beta_{4} + \beta_{2} + \beta_1) q^{13} + (\beta_{6} + \beta_{4} - \beta_1 + 1) q^{14} + ( - \beta_{7} + 4 \beta_{6} + \beta_{5} + 3 \beta_{4} + 4 \beta_{2} + \beta_1) q^{15} + ( - \beta_{4} - 1) q^{16} + ( - \beta_{6} - 2 \beta_{4} + 2 \beta_1 - 2) q^{17} + (2 \beta_{5} + 1) q^{18} + ( - \beta_{7} - \beta_{5} - \beta_{3} - \beta_{2}) q^{20} + ( - 2 \beta_{6} - 2 \beta_{4} - 2 \beta_{3} - 2) q^{21} + (3 \beta_{6} + \beta_{4} + \beta_1 + 1) q^{22} + ( - 3 \beta_{7} - 3 \beta_{6} + 2 \beta_{5} - 4 \beta_{4} - 3 \beta_{2} + 2 \beta_1) q^{23} + (\beta_{6} + \beta_{3}) q^{24} + (2 \beta_{7} + 3 \beta_{6} + 3 \beta_{4} + 3 \beta_{2}) q^{25} + (\beta_{7} - \beta_{5} + \beta_{3} - \beta_{2} + 5) q^{26} + (2 \beta_{5} + 2 \beta_{2} - 2) q^{27} + ( - \beta_{6} + \beta_{5} - \beta_{4} - \beta_{2} + \beta_1) q^{28} + ( - \beta_{7} + 3 \beta_{6} - \beta_{5} + \beta_{4} + 3 \beta_{2} - \beta_1) q^{29} + (\beta_{7} - \beta_{5} + \beta_{3} - 4 \beta_{2} + 3) q^{30} + (\beta_{7} + \beta_{3} + \beta_{2} + 6) q^{31} + \beta_{4} q^{32} + (4 \beta_{6} - 2 \beta_{4} + 4 \beta_1 - 2) q^{33} + (\beta_{6} - 2 \beta_{5} + 2 \beta_{4} + \beta_{2} - 2 \beta_1) q^{34} + ( - \beta_{6} - 2 \beta_{4} - \beta_{3} + 2 \beta_1 - 2) q^{35} + ( - \beta_{4} + 2 \beta_1 - 1) q^{36} + (\beta_{7} - 2 \beta_{5} + \beta_{3} + 1) q^{37} + ( - 4 \beta_{7} - 3 \beta_{5} - 4 \beta_{3} + 3 \beta_{2} - 3) q^{39} + ( - \beta_{6} + \beta_{3} - \beta_1) q^{40} + (2 \beta_{6} + 4 \beta_{4} - 2 \beta_{3} - \beta_1 + 4) q^{41} + ( - 2 \beta_{7} + 2 \beta_{6} + 2 \beta_{4} + 2 \beta_{2}) q^{42} + ( - \beta_{6} + 2 \beta_{4} - \beta_{3} + 2 \beta_1 + 2) q^{43} + ( - 3 \beta_{6} - \beta_{5} - \beta_{4} - 3 \beta_{2} - \beta_1) q^{44} + (\beta_{7} - 3 \beta_{5} + \beta_{3} + \beta_{2} - 6) q^{45} + (3 \beta_{7} - 2 \beta_{5} + 3 \beta_{3} + 3 \beta_{2} - 4) q^{46} + (\beta_{7} + 4 \beta_{6} - \beta_{5} - \beta_{4} + 4 \beta_{2} - \beta_1) q^{47} + (\beta_{7} - \beta_{6} - \beta_{2}) q^{48} + (2 \beta_{7} + 2 \beta_{3} - 3) q^{49} + ( - 2 \beta_{7} - 2 \beta_{3} - 3 \beta_{2} + 3) q^{50} + (4 \beta_{7} - 5 \beta_{6} - \beta_{5} - 3 \beta_{4} - 5 \beta_{2} - \beta_1) q^{51} + ( - \beta_{6} - 5 \beta_{4} - \beta_{3} - \beta_1 - 5) q^{52} + (3 \beta_{7} + 2 \beta_{6} + 3 \beta_{4} + 2 \beta_{2}) q^{53} + (2 \beta_{6} + 2 \beta_{4} + 2 \beta_1 + 2) q^{54} + ( - \beta_{6} + 6 \beta_{4} - 5 \beta_{3} + 6) q^{55} + ( - \beta_{5} + \beta_{2} - 1) q^{56} + (\beta_{7} + \beta_{5} + \beta_{3} - 3 \beta_{2} + 1) q^{58} + (2 \beta_{6} + 3 \beta_{4} + \beta_{3} + \beta_1 + 3) q^{59} + ( - 4 \beta_{6} - 3 \beta_{4} - \beta_{3} - \beta_1 - 3) q^{60} + ( - 2 \beta_{7} + 6 \beta_{6} + \beta_{5} + 3 \beta_{4} + 6 \beta_{2} + \beta_1) q^{61} + (\beta_{6} - 6 \beta_{4} - \beta_{3} - 6) q^{62} + (2 \beta_{7} + \beta_{6} + \beta_{5} - 5 \beta_{4} + \beta_{2} + \beta_1) q^{63} + q^{64} + ( - 7 \beta_{7} - 3 \beta_{5} - 7 \beta_{3} - 2 \beta_{2}) q^{65} + ( - 4 \beta_{6} - 4 \beta_{5} + 2 \beta_{4} - 4 \beta_{2} - 4 \beta_1) q^{66} + ( - 3 \beta_{7} + 3 \beta_{6} + 4 \beta_{4} + 3 \beta_{2}) q^{67} + (2 \beta_{5} - \beta_{2} + 2) q^{68} + (6 \beta_{7} - 2 \beta_{5} + 6 \beta_{3} - 2 \beta_{2} - 4) q^{69} + ( - \beta_{7} + \beta_{6} - 2 \beta_{5} + 2 \beta_{4} + \beta_{2} - 2 \beta_1) q^{70} + ( - 2 \beta_{6} - \beta_{4} + 3 \beta_{3} - 3 \beta_1 - 1) q^{71} + ( - 2 \beta_{5} + \beta_{4} - 2 \beta_1) q^{72} + ( - \beta_{6} + 3 \beta_{4} + 2 \beta_{3} + 3) q^{73} + ( - \beta_{4} - \beta_{3} - 2 \beta_1 - 1) q^{74} + ( - 3 \beta_{7} - \beta_{5} - 3 \beta_{3} - 2 \beta_{2} + 3) q^{75} + (2 \beta_{7} - 2 \beta_{5} + 2 \beta_{3} - 2 \beta_{2} + 2) q^{77} + (3 \beta_{6} + 3 \beta_{4} + 4 \beta_{3} - 3 \beta_1 + 3) q^{78} + (3 \beta_{6} - 4 \beta_{4} + 3 \beta_{3} - 2 \beta_1 - 4) q^{79} + (\beta_{7} + \beta_{6} + \beta_{5} + \beta_{2} + \beta_1) q^{80} + (4 \beta_{6} + 3 \beta_{4} - 2 \beta_1 + 3) q^{81} + ( - 2 \beta_{7} - 2 \beta_{6} + \beta_{5} - 4 \beta_{4} - 2 \beta_{2} + \beta_1) q^{82} + (3 \beta_{7} + 3 \beta_{5} + 3 \beta_{3} - 8 \beta_{2} + 1) q^{83} + (2 \beta_{7} + 2 \beta_{3} - 2 \beta_{2} + 2) q^{84} + (\beta_{7} - \beta_{6} + 4 \beta_{5} - 5 \beta_{4} - \beta_{2} + 4 \beta_1) q^{85} + ( - \beta_{7} + \beta_{6} - 2 \beta_{5} - 2 \beta_{4} + \beta_{2} - 2 \beta_1) q^{86} + ( - 2 \beta_{7} - 3 \beta_{5} - 2 \beta_{3} + \beta_{2} - 7) q^{87} + (\beta_{5} + 3 \beta_{2} - 1) q^{88} + ( - 4 \beta_{7} + 4 \beta_{6} + \beta_{5} - 2 \beta_{4} + 4 \beta_{2} + \beta_1) q^{89} + (\beta_{6} + 6 \beta_{4} - \beta_{3} - 3 \beta_1 + 6) q^{90} + (\beta_{7} - 8 \beta_{6} + 5 \beta_{5} - 5 \beta_{4} - 8 \beta_{2} + 5 \beta_1) q^{91} + (3 \beta_{6} + 4 \beta_{4} - 3 \beta_{3} - 2 \beta_1 + 4) q^{92} + (8 \beta_{6} + 2 \beta_{4} + 6 \beta_{3} + 2) q^{93} + ( - \beta_{7} + \beta_{5} - \beta_{3} - 4 \beta_{2} - 1) q^{94} + ( - \beta_{7} - \beta_{3} + \beta_{2}) q^{96} + ( - 2 \beta_{6} - 8 \beta_{4} + \beta_{3} + 6 \beta_1 - 8) q^{97} + (3 \beta_{4} - 2 \beta_{3} + 3) q^{98} + (6 \beta_{7} - 5 \beta_{6} - 5 \beta_{5} + 3 \beta_{4} - 5 \beta_{2} - 5 \beta_1) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{21} - 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{29} + 8 q^{30} + 52 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} - 20 q^{46} + 12 q^{47} - 2 q^{48} - 24 q^{49} + 12 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} + 4 q^{54} + 26 q^{55} - 4 q^{56} - 4 q^{58} + 8 q^{59} - 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{66} - 10 q^{67} + 12 q^{68} - 40 q^{69} - 6 q^{70} - 4 q^{72} + 14 q^{73} - 4 q^{74} + 16 q^{75} + 8 q^{77} + 6 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} + 8 q^{84} + 18 q^{85} + 10 q^{86} - 52 q^{87} + 4 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} + 10 q^{92} - 8 q^{93} - 24 q^{94} + 4 q^{96} - 28 q^{97} + 12 q^{98} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( \nu^{6} - 15 ) / 20 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( \nu^{7} - 35\nu ) / 20 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( \nu^{6} + 4\nu^{4} + 20\nu^{2} + 5 ) / 20 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( \nu^{7} + 4\nu^{5} + 20\nu^{3} + 5\nu ) / 20 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( \nu^{6} + 8\nu^{4} + 20\nu^{2} + 25 ) / 20 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( \nu^{7} + 6\nu^{5} + 20\nu^{3} + 25\nu ) / 10 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( -\beta_{6} + 2\beta_{4} - \beta_{2} \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( -\beta_{7} + 3\beta_{5} - \beta_{3} \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( 5\beta_{6} - 5\beta_{4} - 5 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( 5\beta_{7} - 10\beta_{5} - 10\beta_1 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( 20\beta_{2} + 15 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( 20\beta_{3} + 35\beta_1 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(\beta_{4}\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
429.1
−0.951057 + 1.64728i
0.587785 1.01807i
0.951057 1.64728i
−0.587785 + 1.01807i
−0.951057 1.64728i
0.587785 + 1.01807i
0.951057 + 1.64728i
−0.587785 1.01807i
−0.500000 + 0.866025i −1.39680 + 2.41933i −0.500000 0.866025i 1.17229 2.03046i −1.39680 2.41933i −1.28408 1.00000 −2.40211 4.16058i 1.17229 + 2.03046i
429.2 −0.500000 + 0.866025i −0.642040 + 1.11205i −0.500000 0.866025i −1.84786 + 3.20059i −0.642040 1.11205i −0.442463 1.00000 0.675571 + 1.17012i −1.84786 3.20059i
429.3 −0.500000 + 0.866025i −0.221232 + 0.383185i −0.500000 0.866025i 0.445746 0.772054i −0.221232 0.383185i 2.52015 1.00000 1.40211 + 2.42853i 0.445746 + 0.772054i
429.4 −0.500000 + 0.866025i 1.26007 2.18251i −0.500000 0.866025i 1.22982 2.13012i 1.26007 + 2.18251i −2.79360 1.00000 −1.67557 2.90217i 1.22982 + 2.13012i
653.1 −0.500000 0.866025i −1.39680 2.41933i −0.500000 + 0.866025i 1.17229 + 2.03046i −1.39680 + 2.41933i −1.28408 1.00000 −2.40211 + 4.16058i 1.17229 2.03046i
653.2 −0.500000 0.866025i −0.642040 1.11205i −0.500000 + 0.866025i −1.84786 3.20059i −0.642040 + 1.11205i −0.442463 1.00000 0.675571 1.17012i −1.84786 + 3.20059i
653.3 −0.500000 0.866025i −0.221232 0.383185i −0.500000 + 0.866025i 0.445746 + 0.772054i −0.221232 + 0.383185i 2.52015 1.00000 1.40211 2.42853i 0.445746 0.772054i
653.4 −0.500000 0.866025i 1.26007 + 2.18251i −0.500000 + 0.866025i 1.22982 + 2.13012i 1.26007 2.18251i −2.79360 1.00000 −1.67557 + 2.90217i 1.22982 2.13012i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 653.4
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 722.2.c.m 8
19.b odd 2 1 722.2.c.n 8
19.c even 3 1 722.2.a.n yes 4
19.c even 3 1 inner 722.2.c.m 8
19.d odd 6 1 722.2.a.m 4
19.d odd 6 1 722.2.c.n 8
19.e even 9 6 722.2.e.r 24
19.f odd 18 6 722.2.e.s 24
57.f even 6 1 6498.2.a.ca 4
57.h odd 6 1 6498.2.a.bx 4
76.f even 6 1 5776.2.a.bv 4
76.g odd 6 1 5776.2.a.bt 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
722.2.a.m 4 19.d odd 6 1
722.2.a.n yes 4 19.c even 3 1
722.2.c.m 8 1.a even 1 1 trivial
722.2.c.m 8 19.c even 3 1 inner
722.2.c.n 8 19.b odd 2 1
722.2.c.n 8 19.d odd 6 1
722.2.e.r 24 19.e even 9 6
722.2.e.s 24 19.f odd 18 6
5776.2.a.bt 4 76.g odd 6 1
5776.2.a.bv 4 76.f even 6 1
6498.2.a.bx 4 57.h odd 6 1
6498.2.a.ca 4 57.f even 6 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(722, [\chi])\):

\( T_{3}^{8} + 2T_{3}^{7} + 10T_{3}^{6} + 12T_{3}^{5} + 64T_{3}^{4} + 88T_{3}^{3} + 120T_{3}^{2} + 48T_{3} + 16 \) Copy content Toggle raw display
\( T_{5}^{8} - 2T_{5}^{7} + 15T_{5}^{6} - 42T_{5}^{5} + 204T_{5}^{4} - 428T_{5}^{3} + 815T_{5}^{2} - 608T_{5} + 361 \) Copy content Toggle raw display
\( T_{7}^{4} + 2T_{7}^{3} - 6T_{7}^{2} - 12T_{7} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{2} + T + 1)^{4} \) Copy content Toggle raw display
$3$ \( T^{8} + 2 T^{7} + 10 T^{6} + 12 T^{5} + \cdots + 16 \) Copy content Toggle raw display
$5$ \( T^{8} - 2 T^{7} + 15 T^{6} - 42 T^{5} + \cdots + 361 \) Copy content Toggle raw display
$7$ \( (T^{4} + 2 T^{3} - 6 T^{2} - 12 T - 4)^{2} \) Copy content Toggle raw display
$11$ \( (T^{4} - 2 T^{3} - 26 T^{2} + 12 T + 76)^{2} \) Copy content Toggle raw display
$13$ \( T^{8} + 18 T^{7} + 215 T^{6} + \cdots + 3721 \) Copy content Toggle raw display
$17$ \( T^{8} + 6 T^{7} + 45 T^{6} + 94 T^{5} + \cdots + 361 \) Copy content Toggle raw display
$19$ \( T^{8} \) Copy content Toggle raw display
$23$ \( T^{8} - 10 T^{7} + 150 T^{6} + \cdots + 1488400 \) Copy content Toggle raw display
$29$ \( T^{8} - 2 T^{7} + 35 T^{6} - 122 T^{5} + \cdots + 361 \) Copy content Toggle raw display
$31$ \( (T^{4} - 26 T^{3} + 246 T^{2} - 996 T + 1436)^{2} \) Copy content Toggle raw display
$37$ \( (T^{4} - 4 T^{3} - 19 T^{2} + 46 T - 19)^{2} \) Copy content Toggle raw display
$41$ \( T^{8} - 12 T^{7} + 125 T^{6} + \cdots + 128881 \) Copy content Toggle raw display
$43$ \( T^{8} - 10 T^{7} + 90 T^{6} + \cdots + 10000 \) Copy content Toggle raw display
$47$ \( T^{8} - 12 T^{7} + 140 T^{6} + \cdots + 5776 \) Copy content Toggle raw display
$53$ \( T^{8} + 8 T^{7} + 95 T^{6} + \cdots + 32761 \) Copy content Toggle raw display
$59$ \( T^{8} - 8 T^{7} + 60 T^{6} + \cdots + 26896 \) Copy content Toggle raw display
$61$ \( T^{8} + 115 T^{6} + 300 T^{5} + \cdots + 1050625 \) Copy content Toggle raw display
$67$ \( T^{8} + 10 T^{7} + 130 T^{6} + \cdots + 400 \) Copy content Toggle raw display
$71$ \( T^{8} + 100 T^{6} - 720 T^{5} + \cdots + 400 \) Copy content Toggle raw display
$73$ \( T^{8} - 14 T^{7} + 145 T^{6} + \cdots + 19321 \) Copy content Toggle raw display
$79$ \( T^{8} + 22 T^{7} + 390 T^{6} + \cdots + 22316176 \) Copy content Toggle raw display
$83$ \( (T^{4} + 12 T^{3} - 196 T^{2} - 2832 T - 6884)^{2} \) Copy content Toggle raw display
$89$ \( T^{8} - 16 T^{7} + 285 T^{6} + \cdots + 1343281 \) Copy content Toggle raw display
$97$ \( T^{8} + 28 T^{7} + 685 T^{6} + \cdots + 63664441 \) Copy content Toggle raw display
show more
show less