↑

Properties

Label 567.2.ba.a.143.10
Level $567$
Weight $2$
Character 567.143
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [567,2,Mod(143,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.ba (of order \(18\), degree \(6\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 143.10
Character \(\chi\) \(=\) 567.143
Dual form 567.2.ba.a.341.10

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.204899 + 0.244189i) q^{2} +(0.329652 + 1.86955i) q^{4} +(2.18935 - 1.83708i) q^{5} +(0.468007 - 2.60403i) q^{7} +(-1.07619 - 0.621337i) q^{8} +0.911030i q^{10} +(2.19030 - 2.61029i) q^{11} +(1.17022 - 3.21516i) q^{13} +(0.539981 + 0.647845i) q^{14} +(-3.19557 + 1.16309i) q^{16} -4.66323 q^{17} -5.52060i q^{19} +(4.15623 + 3.48749i) q^{20} +(0.188615 + 1.06969i) q^{22} +(-0.470293 + 1.29212i) q^{23} +(0.550137 - 3.11998i) q^{25} +(0.545329 + 0.944538i) q^{26} +(5.02264 + 0.0165384i) q^{28} +(2.81504 + 7.73427i) q^{29} +(2.17942 - 0.384290i) q^{31} +(1.22079 - 3.35410i) q^{32} +(0.955489 - 1.13871i) q^{34} +(-3.75918 - 6.56089i) q^{35} +(0.882419 - 1.52840i) q^{37} +(1.34807 + 1.13116i) q^{38} +(-3.49759 + 0.616720i) q^{40} +(4.96713 + 1.80789i) q^{41} +(-1.57831 + 8.95103i) q^{43} +(5.60210 + 3.23437i) q^{44} +(-0.219159 - 0.379594i) q^{46} +(-0.532155 + 3.01800i) q^{47} +(-6.56194 - 2.43741i) q^{49} +(0.649143 + 0.773618i) q^{50} +(6.39667 + 1.12790i) q^{52} +(1.30996 + 0.756305i) q^{53} -9.73859i q^{55} +(-2.12164 + 2.51163i) q^{56} +(-2.46542 - 0.897340i) q^{58} +(6.44995 + 2.34759i) q^{59} +(9.69333 + 1.70919i) q^{61} +(-0.352721 + 0.610930i) q^{62} +(-2.83176 - 4.90475i) q^{64} +(-3.34449 - 9.18891i) q^{65} +(-7.34743 + 6.16523i) q^{67} +(-1.53724 - 8.71812i) q^{68} +(2.37235 + 0.426368i) q^{70} +(9.64722 - 5.56983i) q^{71} +(-5.11937 + 2.95567i) q^{73} +(0.192410 + 0.528643i) q^{74} +(10.3210 - 1.81988i) q^{76} +(-5.77220 - 6.92523i) q^{77} +(8.75642 + 7.34751i) q^{79} +(-4.85952 + 8.41694i) q^{80} +(-1.45922 + 0.842484i) q^{82} +(6.72578 - 2.44798i) q^{83} +(-10.2094 + 8.56673i) q^{85} +(-1.86235 - 2.21946i) q^{86} +(-3.97904 + 1.44825i) q^{88} -12.2586 q^{89} +(-7.82471 - 4.55201i) q^{91} +(-2.57071 - 0.453286i) q^{92} +(-0.627925 - 0.748331i) q^{94} +(-10.1418 - 12.0865i) q^{95} +(2.47531 + 0.436465i) q^{97} +(1.93972 - 1.10293i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\). You can download additional coefficients here.



Currently showing only \(a_p\); display all \(a_n\) Currently showing all \(a_n\); display only \(a_p\)
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.204899 + 0.244189i −0.144885 + 0.172668i −0.833607 − 0.552359i \(-0.813728\pi\)
0.688721 + 0.725026i \(0.258172\pi\)
\(3\) 0 0
\(4\) 0.329652 + 1.86955i 0.164826 + 0.934774i
\(5\) 2.18935 − 1.83708i 0.979106 − 0.821568i −0.00484794 − 0.999988i \(-0.501543\pi\)
0.983954 + 0.178420i \(0.0570987\pi\)
\(6\) 0 0
\(7\) 0.468007 − 2.60403i 0.176890 − 0.984231i
\(8\) −1.07619 − 0.621337i −0.380489 − 0.219676i
\(9\) 0 0
\(10\) 0.911030i 0.288093i
\(11\) 2.19030 − 2.61029i 0.660399 − 0.787033i −0.327044 − 0.945009i \(-0.606053\pi\)
0.987443 + 0.157976i \(0.0504970\pi\)
\(12\) 0 0
\(13\) 1.17022 − 3.21516i 0.324562 − 0.891726i −0.664900 − 0.746932i \(-0.731526\pi\)
0.989462 − 0.144794i \(-0.0462518\pi\)
\(14\) 0.539981 + 0.647845i 0.144316 + 0.173144i
\(15\) 0 0
\(16\) −3.19557 + 1.16309i −0.798893 + 0.290773i
\(17\) −4.66323 −1.13100 −0.565499 − 0.824749i \(-0.691317\pi\)
−0.565499 + 0.824749i \(0.691317\pi\)
\(18\) 0 0
\(19\) − 5.52060i − 1.26651i −0.773942 − 0.633256i \(-0.781718\pi\)
0.773942 − 0.633256i \(-0.218282\pi\)
\(20\) 4.15623 + 3.48749i 0.929362 + 0.779827i
\(21\) 0 0
\(22\) 0.188615 + 1.06969i 0.0402129 + 0.228059i
\(23\) −0.470293 + 1.29212i −0.0980628 + 0.269425i −0.979018 − 0.203775i \(-0.934679\pi\)
0.880955 + 0.473200i \(0.156901\pi\)
\(24\) 0 0
\(25\) 0.550137 − 3.11998i 0.110027 − 0.623997i
\(26\) 0.545329 + 0.944538i 0.106948 + 0.185239i
\(27\) 0 0
\(28\) 5.02264 + 0.0165384i 0.949189 + 0.00312546i
\(29\) 2.81504 + 7.73427i 0.522741 + 1.43622i 0.867458 + 0.497511i \(0.165753\pi\)
−0.344717 + 0.938707i \(0.612025\pi\)
\(30\) 0 0
\(31\) 2.17942 − 0.384290i 0.391435 − 0.0690206i 0.0255331 − 0.999674i \(-0.491872\pi\)
0.365902 + 0.930653i \(0.380761\pi\)
\(32\) 1.22079 − 3.35410i 0.215808 − 0.592927i
\(33\) 0 0
\(34\) 0.955489 − 1.13871i 0.163865 − 0.195287i
\(35\) −3.75918 − 6.56089i −0.635418 − 1.10899i
\(36\) 0 0
\(37\) 0.882419 − 1.52840i 0.145069 − 0.251267i −0.784330 − 0.620344i \(-0.786993\pi\)
0.929399 + 0.369077i \(0.120326\pi\)
\(38\) 1.34807 + 1.13116i 0.218686 + 0.183499i
\(39\) 0 0
\(40\) −3.49759 + 0.616720i −0.553018 + 0.0975120i
\(41\) 4.96713 + 1.80789i 0.775735 + 0.282344i 0.699393 − 0.714737i \(-0.253454\pi\)
0.0763420 + 0.997082i \(0.475676\pi\)
\(42\) 0 0
\(43\) −1.57831 + 8.95103i −0.240690 + 1.36502i 0.589603 + 0.807693i \(0.299284\pi\)
−0.830293 + 0.557327i \(0.811827\pi\)
\(44\) 5.60210 + 3.23437i 0.844548 + 0.487600i
\(45\) 0 0
\(46\) −0.219159 − 0.379594i −0.0323132 − 0.0559681i
\(47\) −0.532155 + 3.01800i −0.0776228 + 0.440221i 0.921083 + 0.389366i \(0.127306\pi\)
−0.998706 + 0.0508551i \(0.983805\pi\)
\(48\) 0 0
\(49\) −6.56194 − 2.43741i −0.937420 − 0.348201i
\(50\) 0.649143 + 0.773618i 0.0918027 + 0.109406i
\(51\) 0 0
\(52\) 6.39667 + 1.12790i 0.887058 + 0.156412i
\(53\) 1.30996 + 0.756305i 0.179937 + 0.103886i 0.587263 − 0.809396i \(-0.300205\pi\)
−0.407326 + 0.913283i \(0.633539\pi\)
\(54\) 0 0
\(55\) − 9.73859i − 1.31315i
\(56\) −2.12164 + 2.51163i −0.283516 + 0.335631i
\(57\) 0 0
\(58\) −2.46542 − 0.897340i −0.323726 − 0.117827i
\(59\) 6.44995 + 2.34759i 0.839713 + 0.305630i 0.725839 − 0.687865i \(-0.241452\pi\)
0.113874 + 0.993495i \(0.463674\pi\)
\(60\) 0 0
\(61\) 9.69333 + 1.70919i 1.24110 + 0.218840i 0.755388 − 0.655277i \(-0.227448\pi\)
0.485715 + 0.874117i \(0.338559\pi\)
\(62\) −0.352721 + 0.610930i −0.0447956 + 0.0775882i
\(63\) 0 0
\(64\) −2.83176 − 4.90475i −0.353970 − 0.613094i
\(65\) −3.34449 − 9.18891i −0.414833 − 1.13974i
\(66\) 0 0
\(67\) −7.34743 + 6.16523i −0.897632 + 0.753203i −0.969726 − 0.244195i \(-0.921476\pi\)
0.0720942 + 0.997398i \(0.477032\pi\)
\(68\) −1.53724 − 8.71812i −0.186418 − 1.05723i
\(69\) 0 0
\(70\) 2.37235 + 0.426368i 0.283550 + 0.0509608i
\(71\) 9.64722 − 5.56983i 1.14491 − 0.661017i 0.197272 − 0.980349i \(-0.436792\pi\)
0.947643 + 0.319332i \(0.103459\pi\)
\(72\) 0 0
\(73\) −5.11937 + 2.95567i −0.599176 + 0.345935i −0.768718 − 0.639588i \(-0.779105\pi\)
0.169541 + 0.985523i \(0.445771\pi\)
\(74\) 0.192410 + 0.528643i 0.0223673 + 0.0614535i
\(75\) 0 0
\(76\) 10.3210 − 1.81988i 1.18390 − 0.208754i
\(77\) −5.77220 − 6.92523i −0.657804 − 0.789203i
\(78\) 0 0
\(79\) 8.75642 + 7.34751i 0.985175 + 0.826660i 0.984862 − 0.173340i \(-0.0554560\pi\)
0.000312673 1.00000i \(0.499900\pi\)
\(80\) −4.85952 + 8.41694i −0.543311 + 0.941042i
\(81\) 0 0
\(82\) −1.45922 + 0.842484i −0.161144 + 0.0930367i
\(83\) 6.72578 − 2.44798i 0.738250 − 0.268701i 0.0545974 − 0.998508i \(-0.482612\pi\)
0.683653 + 0.729807i \(0.260390\pi\)
\(84\) 0 0
\(85\) −10.2094 + 8.56673i −1.10737 + 0.929192i
\(86\) −1.86235 − 2.21946i −0.200822 − 0.239331i
\(87\) 0 0
\(88\) −3.97904 + 1.44825i −0.424167 + 0.154384i
\(89\) −12.2586 −1.29941 −0.649703 − 0.760188i \(-0.725107\pi\)
−0.649703 + 0.760188i \(0.725107\pi\)
\(90\) 0 0
\(91\) −7.82471 − 4.55201i −0.820252 − 0.477181i
\(92\) −2.57071 − 0.453286i −0.268015 − 0.0472583i
\(93\) 0 0
\(94\) −0.627925 − 0.748331i −0.0647655 − 0.0771845i
\(95\) −10.1418 − 12.0865i −1.04053 − 1.24005i
\(96\) 0 0
\(97\) 2.47531 + 0.436465i 0.251330 + 0.0443163i 0.297894 − 0.954599i \(-0.403716\pi\)
−0.0465636 + 0.998915i \(0.514827\pi\)
\(98\) 1.93972 − 1.10293i 0.195941 − 0.111413i
\(99\) 0 0
Currently showing only \(a_p\); display all \(a_n\) Currently showing all \(a_n\); display only \(a_p\)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 567.2.ba.a.143.10 132
3.2 odd 2 189.2.ba.a.101.13 ✓ 132
7.5 odd 6 567.2.bd.a.467.13 132
21.5 even 6 189.2.bd.a.47.10 yes 132
27.4 even 9 189.2.bd.a.185.10 yes 132
27.23 odd 18 567.2.bd.a.17.13 132
189.131 even 18 inner 567.2.ba.a.341.10 132
189.166 odd 18 189.2.ba.a.131.13 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.ba.a.101.13 ✓ 132 3.2 odd 2
189.2.ba.a.131.13 yes 132 189.166 odd 18
189.2.bd.a.47.10 yes 132 21.5 even 6
189.2.bd.a.185.10 yes 132 27.4 even 9
567.2.ba.a.143.10 132 1.1 even 1 trivial
567.2.ba.a.341.10 132 189.131 even 18 inner
567.2.bd.a.17.13 132 27.23 odd 18
567.2.bd.a.467.13 132 7.5 odd 6