Embedded newform 140.3.j.a.27.33

• Label: 140.3.j.a.27.33
• Level: $140$
• Weight: $3$
• Character: 140.27
• Analytic conductor: $3.815$
• Analytic rank: $0$
• Dimension: $88$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.81472370104\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(44\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.33
Character	\(\chi\)	\(=\)	140.27
Dual form			140.3.j.a.83.33

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.34659 - 1.47875i) q^{2} +(-2.39400 + 2.39400i) q^{3} +(-0.373392 - 3.98253i) q^{4} +(-4.78141 + 1.46221i) q^{5} +(0.316387 + 6.76387i) q^{6} +(-3.10178 + 6.27526i) q^{7} +(-6.39197 - 4.81069i) q^{8} -2.46250i q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 16 q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\)	\(57\)	\(71\)	\(101\)
\(\chi(n)\)	\(e\left(\frac{1}{4}\right)\)	\(-1\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.34659	−	1.47875i	0.673295	−	0.739374i
							\(3\)	−2.39400	+	2.39400i	−0.798001	+	0.798001i	−0.982780	−	0.184779i	\(-0.940843\pi\)
0.184779	+	0.982780i	\(0.440843\pi\)
\(5\)	−4.78141	+	1.46221i	−0.956283	+	0.292443i
							\(7\)	−3.10178	+	6.27526i	−0.443112	+	0.896466i
\(11\)			13.1058i			1.19143i								0.803195	+	0.595716i	\(0.203132\pi\)
							−0.803195	+	0.595716i	\(0.796868\pi\)
\(13\)	−11.6097	−	11.6097i	−0.893055	−	0.893055i	0.101754	−	0.994810i	\(-0.467554\pi\)
							−0.994810	+	0.101754i	\(0.967554\pi\)
\(17\)	4.14131	−	4.14131i	0.243607	−	0.243607i	−0.574734	−	0.818340i	\(-0.694894\pi\)
							0.818340	+	0.574734i	\(0.194894\pi\)
\(19\)			23.6531i			1.24490i	0.782660	+	0.622449i	\(0.213862\pi\)
							−0.782660	+	0.622449i	\(0.786138\pi\)
\(23\)	−15.5658	−	15.5658i	−0.676774	−	0.676774i	0.282495	−	0.959269i	\(-0.408838\pi\)
							−0.959269	+	0.282495i	\(0.908838\pi\)
\(29\)		−	11.8899i		−	0.409996i	−0.978762	−	0.204998i	\(-0.934281\pi\)
							0.978762	−	0.204998i	\(-0.0657188\pi\)
\(31\)	26.5108			0.855188			0.427594	−	0.903971i	\(-0.359361\pi\)
							0.427594	+	0.903971i	\(0.359361\pi\)
\(37\)	33.9214	+	33.9214i	0.916795	+	0.916795i	0.996795	−	0.0799998i	\(-0.0254920\pi\)
							−0.0799998	+	0.996795i	\(0.525492\pi\)
\(41\)			37.7893i			0.921691i	0.887480	+	0.460845i	\(0.152454\pi\)
							−0.887480	+	0.460845i	\(0.847546\pi\)
\(43\)	−8.31259	−	8.31259i	−0.193316	−	0.193316i	0.603811	−	0.797127i	\(-0.293648\pi\)
							−0.797127	+	0.603811i	\(0.793648\pi\)
\(47\)	−16.9230	−	16.9230i	−0.360063	−	0.360063i	0.503773	−	0.863836i	\(-0.331945\pi\)
							−0.863836	+	0.503773i	\(0.831945\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.j.a.27.33	yes	88
4.3	odd	2	inner	140.3.j.a.27.12	yes	88
5.3	odd	4	inner	140.3.j.a.83.11	yes	88
7.6	odd	2	inner	140.3.j.a.27.34	yes	88
20.3	even	4	inner	140.3.j.a.83.34	yes	88
28.27	even	2	inner	140.3.j.a.27.11	✓	88
35.13	even	4	inner	140.3.j.a.83.12	yes	88
140.83	odd	4	inner	140.3.j.a.83.33	yes	88

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.j.a.27.11	✓	88	28.27	even	2	inner
140.3.j.a.27.12	yes	88	4.3	odd	2	inner
140.3.j.a.27.33	yes	88	1.1	even	1	trivial
140.3.j.a.27.34	yes	88	7.6	odd	2	inner
140.3.j.a.83.11	yes	88	5.3	odd	4	inner
140.3.j.a.83.12	yes	88	35.13	even	4	inner
140.3.j.a.83.33	yes	88	140.83	odd	4	inner
140.3.j.a.83.34	yes	88	20.3	even	4	inner