Embedded newform 143.4.h.a.14.12

• Label: 143.4.h.a.14.12
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.12
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.88993 - 1.37311i) q^{2} +(-1.38946 - 4.27631i) q^{3} +(-0.785744 + 2.41827i) q^{4} +(-10.3395 - 7.51211i) q^{5} +(-8.49785 - 6.17405i) q^{6} +(-10.5881 + 32.5869i) q^{7} +(7.61067 + 23.4232i) q^{8} +(5.48720 - 3.98669i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.88993	−	1.37311i	0.668191	−	0.485469i	−0.201228	−	0.979544i	\(-0.564493\pi\)
							0.869419	+	0.494075i	\(0.164493\pi\)
\(3\)	−1.38946	−	4.27631i	−0.267401	−	0.822977i	−0.991130	−	0.132893i	\(-0.957573\pi\)
							0.723729	−	0.690084i	\(-0.242427\pi\)
\(5\)	−10.3395	−	7.51211i	−0.924796	−	0.671904i	0.0199169	−	0.999802i	\(-0.493660\pi\)
							−0.944713	+	0.327898i	\(0.893660\pi\)
\(7\)	−10.5881	+	32.5869i	−0.571706	+	1.75953i	0.0754263	+	0.997151i	\(0.475968\pi\)
							−0.647132	+	0.762378i	\(0.724032\pi\)
\(11\)	−36.0558	−	5.56575i	−0.988295	−	0.152558i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	35.8058	+	26.0145i	0.510835	+	0.371143i								0.813140	−	0.582068i	\(-0.197756\pi\)
							−0.302305	+	0.953211i	\(0.597756\pi\)
\(19\)	17.4373	+	53.6666i	0.210547	+	0.647997i	0.999440	+	0.0334665i	\(0.0106547\pi\)
							−0.788893	+	0.614531i	\(0.789345\pi\)
\(23\)	−167.955			−1.52265			−0.761326	−	0.648369i	\(-0.775451\pi\)
							−0.761326	+	0.648369i	\(0.775451\pi\)
\(29\)	54.5003	−	167.735i	0.348981	−	1.07405i	−0.610436	−	0.792065i	\(-0.709006\pi\)
							0.959418	−	0.281989i	\(-0.0909940\pi\)
\(31\)	−147.733	+	107.334i	−0.855924	+	0.621865i	−0.926773	−	0.375622i	\(-0.877429\pi\)
							0.0708492	+	0.997487i	\(0.477429\pi\)
\(37\)	−80.6551	+	248.231i	−0.358368	+	1.10294i	0.595663	+	0.803234i	\(0.296889\pi\)
							−0.954031	+	0.299708i	\(0.903111\pi\)
\(41\)	151.656	+	466.750i	0.577677	+	1.77791i	0.626878	+	0.779117i	\(0.284332\pi\)
							−0.0492018	+	0.998789i	\(0.515668\pi\)
\(43\)	−190.345			−0.675055			−0.337528	−	0.941316i	\(-0.609591\pi\)
							−0.337528	+	0.941316i	\(0.609591\pi\)
\(47\)	−78.6910	−	242.186i	−0.244218	−	0.751627i	−0.995764	−	0.0919456i	\(-0.970691\pi\)
							0.751546	−	0.659681i	\(-0.229309\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.12	✓	68
11.2	odd	10		1573.4.a.p.1.24		34
11.4	even	5	inner	143.4.h.a.92.12	yes	68
11.9	even	5		1573.4.a.o.1.11		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.12	✓	68	1.1	even	1	trivial
143.4.h.a.92.12	yes	68	11.4	even	5	inner
1573.4.a.o.1.11		34	11.9	even	5
1573.4.a.p.1.24		34	11.2	odd	10