Embedded newform 175.4.n.a.29.12

• Label: 175.4.n.a.29.12
• Level: $175$
• Weight: $4$
• Character: 175.29
• Analytic conductor: $10.325$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.3253342510\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.12
Character	\(\chi\)	\(=\)	175.29
Dual form			175.4.n.a.169.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.14628 - 1.02229i) q^{2} +(5.97409 - 8.22263i) q^{3} +(2.38186 + 1.73053i) q^{4} +(9.51619 + 5.86874i) q^{5} +(-27.2020 + 19.7634i) q^{6} +7.00000i q^{7} +(9.83115 + 13.5314i) q^{8} +(-23.5784 - 72.5669i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 192 q^{4} - 46 q^{5} + 386 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\)	\(101\)	\(127\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.14628	−	1.02229i	−1.11238	−	0.361433i	−0.305524	−	0.952184i	\(-0.598832\pi\)
							−0.806854	+	0.590751i	\(0.798832\pi\)
\(3\)	5.97409	−	8.22263i	1.14971	−	1.58245i	0.406111	−	0.913824i	\(-0.366885\pi\)
							0.743603	−	0.668621i	\(-0.233115\pi\)
\(5\)	9.51619	+	5.86874i	0.851154	+	0.524916i
							\(7\)			7.00000i			0.377964i
\(11\)	9.04891	−	27.8497i	0.248032	−	0.763363i								−0.747091	−	0.664721i	\(-0.768550\pi\)
							0.995123	−	0.0986415i	\(-0.0314497\pi\)
\(13\)	63.2889	−	20.5638i	1.35024	−	0.438721i	0.457470	−	0.889225i	\(-0.348756\pi\)
							0.892774	+	0.450504i	\(0.148756\pi\)
\(17\)	−58.0070	−	79.8398i	−0.827575	−	1.13906i	−0.988370	−	0.152071i	\(-0.951406\pi\)
							0.160795	−	0.986988i	\(-0.448594\pi\)
\(19\)	−54.7786	+	39.7990i	−0.661425	+	0.480553i	−0.867144	−	0.498058i	\(-0.834047\pi\)
							0.205719	+	0.978611i	\(0.434047\pi\)
\(23\)	13.5376	+	4.39862i	0.122729	+	0.0398772i	0.369738	−	0.929136i	\(-0.379448\pi\)
							−0.247008	+	0.969013i	\(0.579448\pi\)
\(29\)	56.0150	+	40.6973i	0.358680	+	0.260596i	0.752501	−	0.658591i	\(-0.228847\pi\)
							−0.393821	+	0.919187i	\(0.628847\pi\)
\(31\)	129.176	−	93.8515i	0.748407	−	0.543749i	−0.146926	−	0.989148i	\(-0.546938\pi\)
							0.895333	+	0.445398i	\(0.146938\pi\)
\(37\)	−189.138	+	61.4548i	−0.840382	+	0.273057i	−0.697412	−	0.716670i	\(-0.745665\pi\)
							−0.142970	+	0.989727i	\(0.545665\pi\)
\(41\)	56.8400	+	174.936i	0.216510	+	0.666350i	0.999043	+	0.0437403i	\(0.0139274\pi\)
							−0.782533	+	0.622609i	\(0.786073\pi\)
\(43\)		−	231.141i		−	0.819735i	−0.912145	−	0.409868i	\(-0.865575\pi\)
							0.912145	−	0.409868i	\(-0.134425\pi\)
\(47\)	0.0431285	−	0.0593612i	0.000133850	−	0.000184228i	−0.808950	−	0.587877i	\(-0.799964\pi\)
							0.809084	+	0.587693i	\(0.199964\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.n.a.29.12	✓	184
25.19	even	10	inner	175.4.n.a.169.12	yes	184

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.n.a.29.12	✓	184	1.1	even	1	trivial
175.4.n.a.169.12	yes	184	25.19	even	10	inner