Embedded newform 43.7.f.a.2.18

• Label: 43.7.f.a.2.18
• Level: $43$
• Weight: $7$
• Character: 43.2
• Analytic conductor: $9.892$
• Analytic rank: $0$
• Dimension: $126$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.89232559565\)
Analytic rank:	\(0\)
Dimension:	\(126\)
Relative dimension:	\(21\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			2.18
Character	\(\chi\)	\(=\)	43.2
Dual form			43.7.f.a.22.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(4.32423 + 8.97936i) q^{2} +(20.4277 - 42.4185i) q^{3} +(-22.0266 + 27.6205i) q^{4} +(-183.723 - 41.9336i) q^{5} +469.225 q^{6} -28.9921i q^{7} +(278.591 + 63.5867i) q^{8} +(-927.514 - 1163.07i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{9}{14}\right)\)

Coefficient data

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

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.32423	+	8.97936i	0.540529	+	1.12242i	0.975097	+	0.221781i	\(0.0711869\pi\)
							−0.434568	+	0.900639i	\(0.643099\pi\)
\(3\)	20.4277	−	42.4185i	0.756580	−	1.57105i	−0.0629486	−	0.998017i	\(-0.520050\pi\)
							0.819529	−	0.573038i	\(-0.194235\pi\)
\(5\)	−183.723	−	41.9336i	−1.46979	−	0.335469i	−0.588672	−	0.808372i	\(-0.700349\pi\)
							−0.881114	+	0.472903i	\(0.843206\pi\)
\(7\)		−	28.9921i		−	0.0845250i	−0.999107	−	0.0422625i	\(-0.986543\pi\)
							0.999107	−	0.0422625i	\(-0.0134566\pi\)
\(11\)	−675.300	−	846.799i	−0.507363	−	0.636213i	0.460510	−	0.887655i	\(-0.347667\pi\)
							−0.967872	+	0.251442i	\(0.919095\pi\)
\(13\)	485.731	−	2128.13i	0.221088	−	0.968650i	−0.735573	−	0.677446i	\(-0.763087\pi\)
							0.956661	−	0.291205i	\(-0.0940560\pi\)
\(17\)	−1870.59	−	8195.58i	−0.380743	−	1.66814i	−0.695158	−	0.718857i	\(-0.744666\pi\)
							0.314416	−	0.949285i	\(-0.398191\pi\)
\(19\)	6873.88	+	5481.74i	1.00217	+	0.799203i	0.979685	−	0.200544i	\(-0.0642709\pi\)
							0.0224845	+	0.999747i	\(0.492842\pi\)
\(23\)	7550.77	+	9468.37i	0.620594	+	0.778201i	0.988428	−	0.151691i	\(-0.0484718\pi\)
							−0.367834	+	0.929892i	\(0.619900\pi\)
\(29\)	10457.7	+	21715.6i	0.428788	+	0.890387i	0.997687	+	0.0679796i	\(0.0216553\pi\)
							−0.568899	+	0.822407i	\(0.692630\pi\)
\(31\)	−19566.6	+	9422.77i	−0.656795	+	0.316296i	−0.732433	−	0.680839i	\(-0.761615\pi\)
							0.0756373	+	0.997135i	\(0.475901\pi\)
\(37\)		−	17326.4i		−	0.342062i	−0.985266	−	0.171031i	\(-0.945290\pi\)
							0.985266	−	0.171031i	\(-0.0547098\pi\)
\(41\)	9818.61	−	4728.39i	0.142462	−	0.0686060i	−0.361295	−	0.932452i	\(-0.617665\pi\)
							0.503757	+	0.863846i	\(0.331951\pi\)
\(43\)	58367.1	+	53987.4i	0.734113	+	0.679027i
							\(47\)	84120.6	−	105484.i	0.810231	−	1.01600i	−0.189189	−	0.981941i	\(-0.560586\pi\)
0.999420	−	0.0340568i	\(-0.0108427\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.18	✓	126
43.22	odd	14	inner	43.7.f.a.22.18	yes	126

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.18	✓	126	1.1	even	1	trivial
43.7.f.a.22.18	yes	126	43.22	odd	14	inner