LMFDB - Embedded newform 2667.2.a.p.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [18,-6,-18,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 $ x^18 - 6x^17 - 11x^16 + 123x^15 - 35x^14 - 982x^13 + 988x^12 + 3872x^11 - 5421x^10 - 7882x^9 + 13376x^8 + 7948x^7 - 15795x^6 - 3858x^5 + 8199x^4 + 1453x^3 - 1610x^2 - 380*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.0366427$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.0366427 q^{2} -1.00000 q^{3} -1.99866 q^{4} +1.02187 q^{5} +0.0366427 q^{6} +1.00000 q^{7} +0.146522 q^{8} +1.00000 q^{9} -0.0374440 q^{10} -4.36561 q^{11} +1.99866 q^{12} -3.87219 q^{13} -0.0366427 q^{14} -1.02187 q^{15} +3.99195 q^{16} +6.07872 q^{17} -0.0366427 q^{18} +6.90344 q^{19} -2.04236 q^{20} -1.00000 q^{21} +0.159968 q^{22} -5.17354 q^{23} -0.146522 q^{24} -3.95579 q^{25} +0.141888 q^{26} -1.00000 q^{27} -1.99866 q^{28} -1.01222 q^{29} +0.0374440 q^{30} +8.54462 q^{31} -0.439319 q^{32} +4.36561 q^{33} -0.222741 q^{34} +1.02187 q^{35} -1.99866 q^{36} -8.38368 q^{37} -0.252961 q^{38} +3.87219 q^{39} +0.149726 q^{40} +1.56657 q^{41} +0.0366427 q^{42} -6.37089 q^{43} +8.72536 q^{44} +1.02187 q^{45} +0.189573 q^{46} +4.23682 q^{47} -3.99195 q^{48} +1.00000 q^{49} +0.144951 q^{50} -6.07872 q^{51} +7.73918 q^{52} -5.22125 q^{53} +0.0366427 q^{54} -4.46107 q^{55} +0.146522 q^{56} -6.90344 q^{57} +0.0370905 q^{58} -7.49969 q^{59} +2.04236 q^{60} +14.3692 q^{61} -0.313098 q^{62} +1.00000 q^{63} -7.96779 q^{64} -3.95686 q^{65} -0.159968 q^{66} +7.55792 q^{67} -12.1493 q^{68} +5.17354 q^{69} -0.0374440 q^{70} +15.2047 q^{71} +0.146522 q^{72} -1.99435 q^{73} +0.307201 q^{74} +3.95579 q^{75} -13.7976 q^{76} -4.36561 q^{77} -0.141888 q^{78} -14.9551 q^{79} +4.07924 q^{80} +1.00000 q^{81} -0.0574035 q^{82} -15.0270 q^{83} +1.99866 q^{84} +6.21164 q^{85} +0.233447 q^{86} +1.01222 q^{87} -0.639657 q^{88} -3.14237 q^{89} -0.0374440 q^{90} -3.87219 q^{91} +10.3401 q^{92} -8.54462 q^{93} -0.155249 q^{94} +7.05440 q^{95} +0.439319 q^{96} -16.4469 q^{97} -0.0366427 q^{98} -4.36561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) $ 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

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 $a_p$

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.0366427	−0.0259103	−0.0129552	−	0.999916i	$-0.504124\pi$
$2$	−0.0366427	−0.0259103	−0.0129552	+	0.999916i	$0.504124\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99866	−0.999329
$5$	1.02187	0.456993	0.228497	−	0.973545i	$-0.426619\pi$
$5$	1.02187	0.456993	0.228497	+	0.973545i	$0.426619\pi$
$6$	0.0366427	0.0149593
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.146522	0.0518033
$9$	1.00000	0.333333
$10$	−0.0374440	−0.0118408
$11$	−4.36561	−1.31628	−0.658140	−	0.752895i	$-0.728657\pi$
$11$	−4.36561	−1.31628	−0.658140	+	0.752895i	$0.728657\pi$
$12$	1.99866	0.576963
$13$	−3.87219	−1.07395	−0.536976	−	0.843598i	$-0.680433\pi$
$13$	−3.87219	−1.07395	−0.536976	+	0.843598i	$0.680433\pi$
$14$	−0.0366427	−0.00979319
$15$	−1.02187	−0.263845
$16$	3.99195	0.997986
$17$	6.07872	1.47431	0.737153	−	0.675726i	$-0.236170\pi$
$17$	6.07872	1.47431	0.737153	+	0.675726i	$0.236170\pi$
$18$	−0.0366427	−0.00863678
$19$	6.90344	1.58376	0.791879	−	0.610678i	$-0.209103\pi$
$19$	6.90344	1.58376	0.791879	+	0.610678i	$0.209103\pi$
$20$	−2.04236	−0.456686
$21$	−1.00000	−0.218218
$22$	0.159968	0.0341053
$23$	−5.17354	−1.07876	−0.539379	−	0.842063i	$-0.681341\pi$
$23$	−5.17354	−1.07876	−0.539379	+	0.842063i	$0.681341\pi$
$24$	−0.146522	−0.0299086
$25$	−3.95579	−0.791157
$26$	0.141888	0.0278265
$27$	−1.00000	−0.192450
$28$	−1.99866	−0.377711
$29$	−1.01222	−0.187965	−0.0939823	−	0.995574i	$-0.529960\pi$
$29$	−1.01222	−0.187965	−0.0939823	+	0.995574i	$0.529960\pi$
$30$	0.0374440	0.00683631
$31$	8.54462	1.53466	0.767329	−	0.641253i	$-0.221585\pi$
$31$	8.54462	1.53466	0.767329	+	0.641253i	$0.221585\pi$
$32$	−0.439319	−0.0776614
$33$	4.36561	0.759955
$34$	−0.222741	−0.0381997
$35$	1.02187	0.172727
$36$	−1.99866	−0.333110
$37$	−8.38368	−1.37827	−0.689134	−	0.724634i	$-0.742009\pi$
$37$	−8.38368	−1.37827	−0.689134	+	0.724634i	$0.742009\pi$
$38$	−0.252961	−0.0410357
$39$	3.87219	0.620046
$40$	0.149726	0.0236737
$41$	1.56657	0.244657	0.122329	−	0.992490i	$-0.460964\pi$
$41$	1.56657	0.244657	0.122329	+	0.992490i	$0.460964\pi$
$42$	0.0366427	0.00565410
$43$	−6.37089	−0.971552	−0.485776	−	0.874083i	$-0.661463\pi$
$43$	−6.37089	−0.971552	−0.485776	+	0.874083i	$0.661463\pi$
$44$	8.72536	1.31540
$45$	1.02187	0.152331
$46$	0.189573	0.0279510
$47$	4.23682	0.618003	0.309002	−	0.951062i	$-0.400005\pi$
$47$	4.23682	0.618003	0.309002	+	0.951062i	$0.400005\pi$
$48$	−3.99195	−0.576188
$49$	1.00000	0.142857
$50$	0.144951	0.0204992
$51$	−6.07872	−0.851191
$52$	7.73918	1.07323
$53$	−5.22125	−0.717194	−0.358597	−	0.933492i	$-0.616745\pi$
$53$	−5.22125	−0.717194	−0.358597	+	0.933492i	$0.616745\pi$
$54$	0.0366427	0.00498645
$55$	−4.46107	−0.601531
$56$	0.146522	0.0195798
$57$	−6.90344	−0.914383
$58$	0.0370905	0.00487022
$59$	−7.49969	−0.976377	−0.488188	−	0.872738i	$-0.662342\pi$
$59$	−7.49969	−0.976377	−0.488188	+	0.872738i	$0.662342\pi$
$60$	2.04236	0.263668
$61$	14.3692	1.83979	0.919895	−	0.392165i	$-0.128274\pi$
$61$	14.3692	1.83979	0.919895	+	0.392165i	$0.128274\pi$
$62$	−0.313098	−0.0397635
$63$	1.00000	0.125988
$64$	−7.96779	−0.995974
$65$	−3.95686	−0.490789
$66$	−0.159968	−0.0196907
$67$	7.55792	0.923346	0.461673	−	0.887050i	$-0.347249\pi$
$67$	7.55792	0.923346	0.461673	+	0.887050i	$0.347249\pi$
$68$	−12.1493	−1.47332
$69$	5.17354	0.622821
$70$	−0.0374440	−0.00447542
$71$	15.2047	1.80447	0.902233	−	0.431248i	$-0.141927\pi$
$71$	15.2047	1.80447	0.902233	+	0.431248i	$0.141927\pi$
$72$	0.146522	0.0172678
$73$	−1.99435	−0.233421	−0.116711	−	0.993166i	$-0.537235\pi$
$73$	−1.99435	−0.233421	−0.116711	+	0.993166i	$0.537235\pi$
$74$	0.307201	0.0357114
$75$	3.95579	0.456775
$76$	−13.7976	−1.58269
$77$	−4.36561	−0.497507
$78$	−0.141888	−0.0160656
$79$	−14.9551	−1.68258	−0.841288	−	0.540587i	$-0.818202\pi$
$79$	−14.9551	−1.68258	−0.841288	+	0.540587i	$0.818202\pi$
$80$	4.07924	0.456073
$81$	1.00000	0.111111
$82$	−0.0574035	−0.00633916
$83$	−15.0270	−1.64943	−0.824717	−	0.565546i	$-0.808665\pi$
$83$	−15.0270	−1.64943	−0.824717	+	0.565546i	$0.808665\pi$
$84$	1.99866	0.218071
$85$	6.21164	0.673747
$86$	0.233447	0.0251732
$87$	1.01222	0.108521
$88$	−0.639657	−0.0681876
$89$	−3.14237	−0.333090	−0.166545	−	0.986034i	$-0.553261\pi$
$89$	−3.14237	−0.333090	−0.166545	+	0.986034i	$0.553261\pi$
$90$	−0.0374440	−0.00394695
$91$	−3.87219	−0.405916
$92$	10.3401	1.07803
$93$	−8.54462	−0.886036
$94$	−0.155249	−0.0160127
$95$	7.05440	0.723767
$96$	0.439319	0.0448379
$97$	−16.4469	−1.66993	−0.834966	−	0.550301i	$-0.814513\pi$
$97$	−16.4469	−1.66993	−0.834966	+	0.550301i	$0.814513\pi$
$98$	−0.0366427	−0.00370148
$99$	−4.36561	−0.438760

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	2667.2.a.p.1.10	✓	18
3.2	odd	2		8001.2.a.u.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.p.1.10	✓	18	1.1	even	1	trivial
8001.2.a.u.1.9		18	3.2	odd	2

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0366427 q^{2} -1.00000 q^{3} -1.99866 q^{4} +1.02187 q^{5} +0.0366427 q^{6} +1.00000 q^{7} +0.146522 q^{8} +1.00000 q^{9} -0.0374440 q^{10} -4.36561 q^{11} +1.99866 q^{12} -3.87219 q^{13} -0.0366427 q^{14} -1.02187 q^{15} +3.99195 q^{16} +6.07872 q^{17} -0.0366427 q^{18} +6.90344 q^{19} -2.04236 q^{20} -1.00000 q^{21} +0.159968 q^{22} -5.17354 q^{23} -0.146522 q^{24} -3.95579 q^{25} +0.141888 q^{26} -1.00000 q^{27} -1.99866 q^{28} -1.01222 q^{29} +0.0374440 q^{30} +8.54462 q^{31} -0.439319 q^{32} +4.36561 q^{33} -0.222741 q^{34} +1.02187 q^{35} -1.99866 q^{36} -8.38368 q^{37} -0.252961 q^{38} +3.87219 q^{39} +0.149726 q^{40} +1.56657 q^{41} +0.0366427 q^{42} -6.37089 q^{43} +8.72536 q^{44} +1.02187 q^{45} +0.189573 q^{46} +4.23682 q^{47} -3.99195 q^{48} +1.00000 q^{49} +0.144951 q^{50} -6.07872 q^{51} +7.73918 q^{52} -5.22125 q^{53} +0.0366427 q^{54} -4.46107 q^{55} +0.146522 q^{56} -6.90344 q^{57} +0.0370905 q^{58} -7.49969 q^{59} +2.04236 q^{60} +14.3692 q^{61} -0.313098 q^{62} +1.00000 q^{63} -7.96779 q^{64} -3.95686 q^{65} -0.159968 q^{66} +7.55792 q^{67} -12.1493 q^{68} +5.17354 q^{69} -0.0374440 q^{70} +15.2047 q^{71} +0.146522 q^{72} -1.99435 q^{73} +0.307201 q^{74} +3.95579 q^{75} -13.7976 q^{76} -4.36561 q^{77} -0.141888 q^{78} -14.9551 q^{79} +4.07924 q^{80} +1.00000 q^{81} -0.0574035 q^{82} -15.0270 q^{83} +1.99866 q^{84} +6.21164 q^{85} +0.233447 q^{86} +1.01222 q^{87} -0.639657 q^{88} -3.14237 q^{89} -0.0374440 q^{90} -3.87219 q^{91} +10.3401 q^{92} -8.54462 q^{93} -0.155249 q^{94} +7.05440 q^{95} +0.439319 q^{96} -16.4469 q^{97} -0.0366427 q^{98} -4.36561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

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