Embedded newform 175.3.m.a.34.17

• Label: 175.3.m.a.34.17
• Level: $175$
• Weight: $3$
• Character: 175.34
• Analytic conductor: $4.768$
• Analytic rank: $0$
• Dimension: $152$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	175.m (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.76840462631\)
Analytic rank:	\(0\)
Dimension:	\(152\)
Relative dimension:	\(38\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			34.17
Character	\(\chi\)	\(=\)	175.34
Dual form			175.3.m.a.139.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.405562 + 0.558208i) q^{2} +(-0.878315 - 2.70318i) q^{3} +(1.08895 + 3.35145i) q^{4} +(-4.39662 - 2.38112i) q^{5} +(1.86515 + 0.606023i) q^{6} +(1.23529 + 6.89014i) q^{7} +(-4.93729 - 1.60422i) q^{8} +(0.745425 - 0.541583i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 10 q^{2} + 66 q^{4} - 40 q^{8} - 108 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(101\)	\(127\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.405562	+	0.558208i	−0.202781	+	0.279104i	−0.898280	−	0.439423i	\(-0.855183\pi\)
							0.695500	+	0.718526i	\(0.255183\pi\)
\(3\)	−0.878315	−	2.70318i	−0.292772	−	0.901059i	−0.983961	−	0.178385i	\(-0.942913\pi\)
							0.691189	−	0.722674i	\(-0.257087\pi\)
\(5\)	−4.39662	−	2.38112i	−0.879324	−	0.476224i
							\(7\)	1.23529	+	6.89014i	0.176470	+	0.984306i
\(11\)	−7.57246	−	5.50171i	−0.688405	−	0.500156i								0.187730	−	0.982221i	\(-0.439887\pi\)
							−0.876136	+	0.482065i	\(0.839887\pi\)
\(13\)	−19.1563	+	13.9179i	−1.47356	+	1.07061i	−0.494002	+	0.869461i	\(0.664466\pi\)
							−0.979561	+	0.201145i	\(0.935534\pi\)
\(17\)	−5.39205	+	16.5950i	−0.317179	+	0.976177i	0.657669	+	0.753307i	\(0.271543\pi\)
							−0.974848	+	0.222870i	\(0.928457\pi\)
\(19\)	12.3757	+	4.02111i	0.651352	+	0.211637i	0.616010	−	0.787738i	\(-0.288748\pi\)
							0.0353421	+	0.999375i	\(0.488748\pi\)
\(23\)	−18.5421	+	25.5210i	−0.806179	+	1.10961i	0.185723	+	0.982602i	\(0.440537\pi\)
							−0.991902	+	0.127008i	\(0.959463\pi\)
\(29\)	−8.92365	−	27.4642i	−0.307712	−	0.947040i	−0.978651	−	0.205528i	\(-0.934109\pi\)
							0.670939	−	0.741512i	\(-0.265891\pi\)
\(31\)	−6.13108	−	1.99211i	−0.197777	−	0.0642616i	0.208454	−	0.978032i	\(-0.433157\pi\)
							−0.406230	+	0.913771i	\(0.633157\pi\)
\(37\)	26.4076	+	36.3469i	0.713718	+	0.982348i	0.999709	+	0.0241162i	\(0.00767715\pi\)
							−0.285991	+	0.958232i	\(0.592323\pi\)
\(41\)	−9.77586	−	13.4553i	−0.238436	−	0.328178i	0.672984	−	0.739657i	\(-0.265012\pi\)
							−0.911419	+	0.411479i	\(0.865012\pi\)
\(43\)		−	68.0592i		−	1.58277i	−0.611317	−	0.791386i	\(-0.709360\pi\)
							0.611317	−	0.791386i	\(-0.290640\pi\)
\(47\)	−5.17108	−	15.9149i	−0.110023	−	0.338616i	0.880854	−	0.473389i	\(-0.156969\pi\)
							−0.990876	+	0.134773i	\(0.956969\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.3.m.a.34.17	✓	152
7.6	odd	2	inner	175.3.m.a.34.18	yes	152
25.14	even	10	inner	175.3.m.a.139.18	yes	152
175.139	odd	10	inner	175.3.m.a.139.17	yes	152

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.3.m.a.34.17	✓	152	1.1	even	1	trivial
175.3.m.a.34.18	yes	152	7.6	odd	2	inner
175.3.m.a.139.17	yes	152	175.139	odd	10	inner
175.3.m.a.139.18	yes	152	25.14	even	10	inner