Embedded newform 151.2.h.a.94.1

• Label: 151.2.h.a.94.1
• Level: $151$
• Weight: $2$
• Character: 151.94
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.h (of order \(25\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(11\) over \(\Q(\zeta_{25})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			94.1
Character	\(\chi\)	\(=\)	151.94
Dual form			151.2.h.a.98.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.13214 + 1.54909i) q^{2} +(0.247866 - 0.136266i) q^{3} +(1.52830 - 4.70361i) q^{4} +(-0.795046 + 1.25279i) q^{5} +(-0.317397 + 0.674503i) q^{6} +(3.32004 - 1.31450i) q^{7} +(2.39896 + 7.38325i) q^{8} +(-1.56461 + 2.46543i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{16}{25}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.13214	+	1.54909i	−1.50765	+	1.09537i	−0.540440	+	0.841383i	\(0.681742\pi\)
							−0.967208	+	0.253987i	\(0.918258\pi\)
\(3\)	0.247866	−	0.136266i	0.143106	−	0.0786729i	−0.408592	−	0.912717i	\(-0.633980\pi\)
							0.551698	+	0.834044i	\(0.313980\pi\)
\(5\)	−0.795046	+	1.25279i	−0.355555	+	0.560265i	−0.974280	−	0.225343i	\(-0.927650\pi\)
							0.618724	+	0.785608i	\(0.287650\pi\)
\(7\)	3.32004	−	1.31450i	1.25486	−	0.496833i	0.355758	−	0.934578i	\(-0.384223\pi\)
							0.899099	+	0.437745i	\(0.144223\pi\)
\(11\)	3.36272	+	1.84867i	1.01390	+	0.557395i	0.899905	−	0.436087i	\(-0.143636\pi\)
							0.113993	+	0.993482i	\(0.463636\pi\)
\(13\)	0.629279	+	0.590932i	0.174530	+	0.163895i	0.766890	−	0.641779i	\(-0.221803\pi\)
							−0.592359	+	0.805674i	\(0.701803\pi\)
\(17\)	−2.39582	−	0.948574i	−0.581073	−	0.230063i	0.0591541	−	0.998249i	\(-0.481160\pi\)
							−0.640227	+	0.768186i	\(0.721160\pi\)
\(19\)	−2.42885	+	7.47522i	−0.557215	+	1.71493i	0.132804	+	0.991142i	\(0.457602\pi\)
							−0.690020	+	0.723791i	\(0.742398\pi\)
\(23\)	1.19620	−	3.68153i	0.249426	−	0.767653i	−0.745451	−	0.666560i	\(-0.767766\pi\)
							0.994877	−	0.101093i	\(-0.0322339\pi\)
\(29\)	2.88402	−	0.364336i	0.535548	−	0.0676555i	0.147092	−	0.989123i	\(-0.453009\pi\)
							0.388456	+	0.921467i	\(0.373009\pi\)
\(31\)	9.93228	−	2.55018i	1.78389	−	0.458025i	0.794992	−	0.606620i	\(-0.207475\pi\)
							0.988898	+	0.148595i	\(0.0474752\pi\)
\(37\)	−0.763689	−	0.717152i	−0.125550	−	0.117899i	0.619229	−	0.785210i	\(-0.287445\pi\)
							−0.744779	+	0.667311i	\(0.767445\pi\)
\(41\)	2.82049	−	5.99384i	0.440486	−	0.936081i	−0.554128	−	0.832432i	\(-0.686948\pi\)
							0.994614	−	0.103649i	\(-0.0330519\pi\)
\(43\)	−7.71346	−	3.05398i	−1.17629	−	0.465727i	−0.303031	−	0.952981i	\(-0.597999\pi\)
							−0.873260	+	0.487254i	\(0.837999\pi\)
\(47\)	−1.35885	+	2.88771i	−0.198209	+	0.421216i	−0.979080	−	0.203477i	\(-0.934776\pi\)
							0.780871	+	0.624693i	\(0.214776\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.h.a.94.1	✓	220
151.98	even	25	inner	151.2.h.a.98.1	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.h.a.94.1	✓	220	1.1	even	1	trivial
151.2.h.a.98.1	yes	220	151.98	even	25	inner