Embedded newform 43.11.d.a.7.20

• Label: 43.11.d.a.7.20
• Level: $43$
• Weight: $11$
• Character: 43.7
• Analytic conductor: $27.320$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3203618650\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.20
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+7.11093i q^{2} +(-393.634 + 227.264i) q^{3} +973.435 q^{4} +(-1943.65 + 1122.17i) q^{5} +(-1616.06 - 2799.10i) q^{6} +(8908.31 + 5143.21i) q^{7} +14203.6i q^{8} +(73773.8 - 127780. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)			7.11093i			0.222217i	0.993808	+	0.111108i	\(0.0354400\pi\)
							−0.993808	+	0.111108i	\(0.964560\pi\)
\(3\)	−393.634	+	227.264i	−1.61989	+	0.935245i	−0.632945	+	0.774197i	\(0.718154\pi\)
							−0.986947	+	0.161048i	\(0.948513\pi\)
\(5\)	−1943.65	+	1122.17i	−0.621969	+	0.359094i	−0.777635	−	0.628716i	\(-0.783581\pi\)
							0.155666	+	0.987810i	\(0.450248\pi\)
\(7\)	8908.31	+	5143.21i	0.530036	+	0.306016i	0.741031	−	0.671471i	\(-0.234337\pi\)
							−0.210995	+	0.977487i	\(0.567670\pi\)
\(11\)	229447.			1.42468			0.712342	−	0.701832i	\(-0.247634\pi\)
							0.712342	+	0.701832i	\(0.247634\pi\)
\(13\)	52326.5	−	90632.2i	0.140931	−	0.244099i	−0.786917	−	0.617059i	\(-0.788324\pi\)
							0.927847	+	0.372960i	\(0.121657\pi\)
\(17\)	978422.	−	1.69468e6i	0.689099	−	1.19355i	−0.283031	−	0.959111i	\(-0.591340\pi\)
							0.972130	−	0.234444i	\(-0.0753268\pi\)
\(19\)	97267.8	−	56157.6i	0.0392827	−	0.0226799i	−0.480230	−	0.877143i	\(-0.659447\pi\)
							0.519513	+	0.854463i	\(0.326113\pi\)
\(23\)	2.53285e6	+	4.38702e6i	0.393522	+	0.681601i	0.992911	−	0.118857i	\(-0.0379230\pi\)
							−0.599389	+	0.800458i	\(0.704590\pi\)
\(29\)	1.83129e6	+	1.05729e6i	0.0892825	+	0.0515472i	0.543977	−	0.839100i	\(-0.316918\pi\)
							−0.454694	+	0.890648i	\(0.650251\pi\)
\(31\)	3.80864e6	+	6.59676e6i	0.133034	+	0.230421i	0.924845	−	0.380345i	\(-0.124195\pi\)
							−0.791811	+	0.610766i	\(0.790861\pi\)
\(37\)	2.72842e7	−	1.57526e7i	0.393462	−	0.227166i	−0.290197	−	0.956967i	\(-0.593721\pi\)
							0.683659	+	0.729801i	\(0.260387\pi\)
\(41\)	2.35433e7			0.203211			0.101606	−	0.994825i	\(-0.467602\pi\)
							0.101606	+	0.994825i	\(0.467602\pi\)
\(43\)	1.46853e8	+	6.76718e6i	0.998940	+	0.0460326i
							\(47\)	−2.97050e8			−1.29521			−0.647606	−	0.761976i	\(-0.724230\pi\)
−0.647606	+	0.761976i	\(0.724230\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.20	✓	72
43.37	odd	6	inner	43.11.d.a.37.17	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.20	✓	72	1.1	even	1	trivial
43.11.d.a.37.17	yes	72	43.37	odd	6	inner