LMFDB - Embedded newform 2667.2.a.p.1.18

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			1.18
Root			$-2.55461$ 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)

$f(q)$	$=$	\(q+2.55461 q^{2} -1.00000 q^{3} +4.52602 q^{4} -2.12871 q^{5} -2.55461 q^{6} +1.00000 q^{7} +6.45298 q^{8} +1.00000 q^{9} -5.43801 q^{10} -4.13995 q^{11} -4.52602 q^{12} -4.75071 q^{13} +2.55461 q^{14} +2.12871 q^{15} +7.43278 q^{16} -1.32611 q^{17} +2.55461 q^{18} -5.03962 q^{19} -9.63456 q^{20} -1.00000 q^{21} -10.5759 q^{22} +0.634865 q^{23} -6.45298 q^{24} -0.468604 q^{25} -12.1362 q^{26} -1.00000 q^{27} +4.52602 q^{28} -6.95445 q^{29} +5.43801 q^{30} -3.31737 q^{31} +6.08189 q^{32} +4.13995 q^{33} -3.38770 q^{34} -2.12871 q^{35} +4.52602 q^{36} +7.32426 q^{37} -12.8742 q^{38} +4.75071 q^{39} -13.7365 q^{40} +4.92704 q^{41} -2.55461 q^{42} -0.118376 q^{43} -18.7375 q^{44} -2.12871 q^{45} +1.62183 q^{46} +10.6971 q^{47} -7.43278 q^{48} +1.00000 q^{49} -1.19710 q^{50} +1.32611 q^{51} -21.5018 q^{52} +4.29353 q^{53} -2.55461 q^{54} +8.81274 q^{55} +6.45298 q^{56} +5.03962 q^{57} -17.7659 q^{58} -9.53007 q^{59} +9.63456 q^{60} -9.70203 q^{61} -8.47457 q^{62} +1.00000 q^{63} +0.671262 q^{64} +10.1129 q^{65} +10.5759 q^{66} +2.95734 q^{67} -6.00202 q^{68} -0.634865 q^{69} -5.43801 q^{70} +1.45245 q^{71} +6.45298 q^{72} +7.08465 q^{73} +18.7106 q^{74} +0.468604 q^{75} -22.8094 q^{76} -4.13995 q^{77} +12.1362 q^{78} +5.36766 q^{79} -15.8222 q^{80} +1.00000 q^{81} +12.5867 q^{82} -10.4852 q^{83} -4.52602 q^{84} +2.82291 q^{85} -0.302403 q^{86} +6.95445 q^{87} -26.7150 q^{88} -3.15112 q^{89} -5.43801 q^{90} -4.75071 q^{91} +2.87341 q^{92} +3.31737 q^{93} +27.3270 q^{94} +10.7279 q^{95} -6.08189 q^{96} -16.7425 q^{97} +2.55461 q^{98} -4.13995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.55461	1.80638	0.903190	−	0.429241i	$-0.141219\pi$
$2$	2.55461	1.80638	0.903190	+	0.429241i	$0.141219\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.52602	2.26301
$5$	−2.12871	−0.951987	−0.475993	−	0.879449i	$-0.657911\pi$
$5$	−2.12871	−0.951987	−0.475993	+	0.879449i	$0.657911\pi$
$6$	−2.55461	−1.04291
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	6.45298	2.28147
$9$	1.00000	0.333333
$10$	−5.43801	−1.71965
$11$	−4.13995	−1.24824	−0.624121	−	0.781328i	$-0.714543\pi$
$11$	−4.13995	−1.24824	−0.624121	+	0.781328i	$0.714543\pi$
$12$	−4.52602	−1.30655
$13$	−4.75071	−1.31761	−0.658805	−	0.752313i	$-0.728938\pi$
$13$	−4.75071	−1.31761	−0.658805	+	0.752313i	$0.728938\pi$
$14$	2.55461	0.682747
$15$	2.12871	0.549630
$16$	7.43278	1.85820
$17$	−1.32611	−0.321630	−0.160815	−	0.986985i	$-0.551412\pi$
$17$	−1.32611	−0.321630	−0.160815	+	0.986985i	$0.551412\pi$
$18$	2.55461	0.602127
$19$	−5.03962	−1.15617	−0.578083	−	0.815978i	$-0.696199\pi$
$19$	−5.03962	−1.15617	−0.578083	+	0.815978i	$0.696199\pi$
$20$	−9.63456	−2.15435
$21$	−1.00000	−0.218218
$22$	−10.5759	−2.25480
$23$	0.634865	0.132378	0.0661892	−	0.997807i	$-0.478916\pi$
$23$	0.634865	0.132378	0.0661892	+	0.997807i	$0.478916\pi$
$24$	−6.45298	−1.31721
$25$	−0.468604	−0.0937208
$26$	−12.1362	−2.38011
$27$	−1.00000	−0.192450
$28$	4.52602	0.855336
$29$	−6.95445	−1.29141	−0.645705	−	0.763587i	$-0.723436\pi$
$29$	−6.95445	−1.29141	−0.645705	+	0.763587i	$0.723436\pi$
$30$	5.43801	0.992840
$31$	−3.31737	−0.595817	−0.297908	−	0.954594i	$-0.596289\pi$
$31$	−3.31737	−0.595817	−0.297908	+	0.954594i	$0.596289\pi$
$32$	6.08189	1.07514
$33$	4.13995	0.720673
$34$	−3.38770	−0.580986
$35$	−2.12871	−0.359817
$36$	4.52602	0.754336
$37$	7.32426	1.20410	0.602051	−	0.798458i	$-0.294350\pi$
$37$	7.32426	1.20410	0.602051	+	0.798458i	$0.294350\pi$
$38$	−12.8742	−2.08848
$39$	4.75071	0.760723
$40$	−13.7365	−2.17193
$41$	4.92704	0.769475	0.384737	−	0.923026i	$-0.374292\pi$
$41$	4.92704	0.769475	0.384737	+	0.923026i	$0.374292\pi$
$42$	−2.55461	−0.394184
$43$	−0.118376	−0.0180521	−0.00902606	−	0.999959i	$-0.502873\pi$
$43$	−0.118376	−0.0180521	−0.00902606	+	0.999959i	$0.502873\pi$
$44$	−18.7375	−2.82478
$45$	−2.12871	−0.317329
$46$	1.62183	0.239126
$47$	10.6971	1.56034	0.780169	−	0.625568i	$-0.215133\pi$
$47$	10.6971	1.56034	0.780169	+	0.625568i	$0.215133\pi$
$48$	−7.43278	−1.07283
$49$	1.00000	0.142857
$50$	−1.19710	−0.169295
$51$	1.32611	0.185693
$52$	−21.5018	−2.98176
$53$	4.29353	0.589762	0.294881	−	0.955534i	$-0.404720\pi$
$53$	4.29353	0.589762	0.294881	+	0.955534i	$0.404720\pi$
$54$	−2.55461	−0.347638
$55$	8.81274	1.18831
$56$	6.45298	0.862315
$57$	5.03962	0.667513
$58$	−17.7659	−2.33278
$59$	−9.53007	−1.24071	−0.620355	−	0.784321i	$-0.713011\pi$
$59$	−9.53007	−1.24071	−0.620355	+	0.784321i	$0.713011\pi$
$60$	9.63456	1.24382
$61$	−9.70203	−1.24222	−0.621109	−	0.783724i	$-0.713318\pi$
$61$	−9.70203	−1.24222	−0.621109	+	0.783724i	$0.713318\pi$
$62$	−8.47457	−1.07627
$63$	1.00000	0.125988
$64$	0.671262	0.0839078
$65$	10.1129	1.25435
$66$	10.5759	1.30181
$67$	2.95734	0.361297	0.180648	−	0.983548i	$-0.442180\pi$
$67$	2.95734	0.361297	0.180648	+	0.983548i	$0.442180\pi$
$68$	−6.00202	−0.727851
$69$	−0.634865	−0.0764288
$70$	−5.43801	−0.649967
$71$	1.45245	0.172375	0.0861873	−	0.996279i	$-0.472532\pi$
$71$	1.45245	0.172375	0.0861873	+	0.996279i	$0.472532\pi$
$72$	6.45298	0.760490
$73$	7.08465	0.829195	0.414598	−	0.910005i	$-0.363922\pi$
$73$	7.08465	0.829195	0.414598	+	0.910005i	$0.363922\pi$
$74$	18.7106	2.17506
$75$	0.468604	0.0541097
$76$	−22.8094	−2.61641
$77$	−4.13995	−0.471791
$78$	12.1362	1.37415
$79$	5.36766	0.603909	0.301954	−	0.953322i	$-0.402361\pi$
$79$	5.36766	0.603909	0.301954	+	0.953322i	$0.402361\pi$
$80$	−15.8222	−1.76898
$81$	1.00000	0.111111
$82$	12.5867	1.38996
$83$	−10.4852	−1.15090	−0.575451	−	0.817836i	$-0.695174\pi$
$83$	−10.4852	−1.15090	−0.575451	+	0.817836i	$0.695174\pi$
$84$	−4.52602	−0.493829
$85$	2.82291	0.306188
$86$	−0.302403	−0.0326090
$87$	6.95445	0.745595
$88$	−26.7150	−2.84783
$89$	−3.15112	−0.334018	−0.167009	−	0.985955i	$-0.553411\pi$
$89$	−3.15112	−0.334018	−0.167009	+	0.985955i	$0.553411\pi$
$90$	−5.43801	−0.573217
$91$	−4.75071	−0.498010
$92$	2.87341	0.299574
$93$	3.31737	0.343995
$94$	27.3270	2.81856
$95$	10.7279	1.10066
$96$	−6.08189	−0.620730
$97$	−16.7425	−1.69994	−0.849970	−	0.526831i	$-0.823380\pi$
$97$	−16.7425	−1.69994	−0.849970	+	0.526831i	$0.823380\pi$
$98$	2.55461	0.258054
$99$	−4.13995	−0.416081

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.1.18	✓	18
3.2	odd	2		8001.2.a.u.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.p.1.18	✓	18	1.1	even	1	trivial
8001.2.a.u.1.1		18	3.2	odd	2

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Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+2.55461 q^{2} -1.00000 q^{3} +4.52602 q^{4} -2.12871 q^{5} -2.55461 q^{6} +1.00000 q^{7} +6.45298 q^{8} +1.00000 q^{9} -5.43801 q^{10} -4.13995 q^{11} -4.52602 q^{12} -4.75071 q^{13} +2.55461 q^{14} +2.12871 q^{15} +7.43278 q^{16} -1.32611 q^{17} +2.55461 q^{18} -5.03962 q^{19} -9.63456 q^{20} -1.00000 q^{21} -10.5759 q^{22} +0.634865 q^{23} -6.45298 q^{24} -0.468604 q^{25} -12.1362 q^{26} -1.00000 q^{27} +4.52602 q^{28} -6.95445 q^{29} +5.43801 q^{30} -3.31737 q^{31} +6.08189 q^{32} +4.13995 q^{33} -3.38770 q^{34} -2.12871 q^{35} +4.52602 q^{36} +7.32426 q^{37} -12.8742 q^{38} +4.75071 q^{39} -13.7365 q^{40} +4.92704 q^{41} -2.55461 q^{42} -0.118376 q^{43} -18.7375 q^{44} -2.12871 q^{45} +1.62183 q^{46} +10.6971 q^{47} -7.43278 q^{48} +1.00000 q^{49} -1.19710 q^{50} +1.32611 q^{51} -21.5018 q^{52} +4.29353 q^{53} -2.55461 q^{54} +8.81274 q^{55} +6.45298 q^{56} +5.03962 q^{57} -17.7659 q^{58} -9.53007 q^{59} +9.63456 q^{60} -9.70203 q^{61} -8.47457 q^{62} +1.00000 q^{63} +0.671262 q^{64} +10.1129 q^{65} +10.5759 q^{66} +2.95734 q^{67} -6.00202 q^{68} -0.634865 q^{69} -5.43801 q^{70} +1.45245 q^{71} +6.45298 q^{72} +7.08465 q^{73} +18.7106 q^{74} +0.468604 q^{75} -22.8094 q^{76} -4.13995 q^{77} +12.1362 q^{78} +5.36766 q^{79} -15.8222 q^{80} +1.00000 q^{81} +12.5867 q^{82} -10.4852 q^{83} -4.52602 q^{84} +2.82291 q^{85} -0.302403 q^{86} +6.95445 q^{87} -26.7150 q^{88} -3.15112 q^{89} -5.43801 q^{90} -4.75071 q^{91} +2.87341 q^{92} +3.31737 q^{93} +27.3270 q^{94} +10.7279 q^{95} -6.08189 q^{96} -16.7425 q^{97} +2.55461 q^{98} -4.13995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 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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