Embedded newform 43.5.d.a.7.14

• Label: 43.5.d.a.7.14
• Level: $43$
• Weight: $5$
• Character: 43.7
• Analytic conductor: $4.445$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.44490841261\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.14
Character	\(\chi\)	\(=\)	43.7
Dual form			43.5.d.a.37.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+6.75666i q^{2} +(-1.02237 + 0.590266i) q^{3} -29.6524 q^{4} +(-6.96733 + 4.02259i) q^{5} +(-3.98823 - 6.90781i) q^{6} +(-45.3584 - 26.1877i) q^{7} -92.2449i q^{8} +(-39.8032 + 68.9411i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)			6.75666i			1.68916i	0.535426	+	0.844582i	\(0.320151\pi\)
							−0.535426	+	0.844582i	\(0.679849\pi\)
\(3\)	−1.02237	+	0.590266i	−0.113597	+	0.0655851i	−0.555722	−	0.831368i	\(-0.687558\pi\)
							0.442125	+	0.896953i	\(0.354225\pi\)
\(5\)	−6.96733	+	4.02259i	−0.278693	+	0.160904i	−0.632832	−	0.774289i	\(-0.718108\pi\)
							0.354138	+	0.935193i	\(0.384774\pi\)
\(7\)	−45.3584	−	26.1877i	−0.925681	−	0.534442i	−0.0402380	−	0.999190i	\(-0.512812\pi\)
							−0.885443	+	0.464748i	\(0.846145\pi\)
\(11\)	122.533			1.01267			0.506334	−	0.862337i	\(-0.331000\pi\)
							0.506334	+	0.862337i	\(0.331000\pi\)
\(13\)	5.29510	−	9.17138i	0.0313319	−	0.0542685i	−0.849934	−	0.526889i	\(-0.823358\pi\)
							0.881266	+	0.472620i	\(0.156692\pi\)
\(17\)	−156.713	+	271.436i	−0.542261	+	0.939224i	0.456513	+	0.889717i	\(0.349098\pi\)
							−0.998774	+	0.0495070i	\(0.984235\pi\)
\(19\)	−221.553	+	127.914i	−0.613720	+	0.354332i	−0.774420	−	0.632672i	\(-0.781958\pi\)
							0.160700	+	0.987003i	\(0.448625\pi\)
\(23\)	177.642	+	307.685i	0.335808	+	0.581636i	0.983640	−	0.180147i	\(-0.0576574\pi\)
							−0.647832	+	0.761783i	\(0.724324\pi\)
\(29\)	−351.256	−	202.798i	−0.417664	−	0.241139i	0.276413	−	0.961039i	\(-0.410854\pi\)
							−0.694077	+	0.719900i	\(0.744187\pi\)
\(31\)	412.566	+	714.585i	0.429309	+	0.743585i	0.996812	−	0.0797864i	\(-0.0254238\pi\)
							−0.567503	+	0.823371i	\(0.692090\pi\)
\(37\)	1127.35	−	650.876i	0.823485	−	0.475439i	−0.0281320	−	0.999604i	\(-0.508956\pi\)
							0.851617	+	0.524165i	\(0.175623\pi\)
\(41\)	958.461			0.570173			0.285086	−	0.958502i	\(-0.407978\pi\)
							0.285086	+	0.958502i	\(0.407978\pi\)
\(43\)	1295.42	+	1319.35i	0.700605	+	0.713549i
							\(47\)	1729.47			0.782921			0.391460	−	0.920195i	\(-0.371970\pi\)
0.391460	+	0.920195i	\(0.371970\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.d.a.7.14	✓	28
43.37	odd	6	inner	43.5.d.a.37.1	yes	28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.d.a.7.14	✓	28	1.1	even	1	trivial
43.5.d.a.37.1	yes	28	43.37	odd	6	inner