Embedded newform 151.2.d.b.59.2

• Label: 151.2.d.b.59.2
• Level: $151$
• Weight: $2$
• Character: 151.59
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.d (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			59.2
Character	\(\chi\)	\(=\)	151.59
Dual form			151.2.d.b.64.2

$q$-expansion

\(f(q)\)	\(=\)	\(q-1.66254 q^{2} +(-0.661185 - 0.480379i) q^{3} +0.764034 q^{4} +(0.441151 + 1.35772i) q^{5} +(1.09925 + 0.798648i) q^{6} +(-0.446078 - 1.37289i) q^{7} +2.05484 q^{8} +(-0.720649 - 2.21793i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + q^{3} + 22 q^{4} - 19 q^{6} + 2 q^{7} + 18 q^{8} - 15 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{1}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.66254			−1.17559			−0.587796	−	0.809009i	\(-0.700004\pi\)
							−0.587796	+	0.809009i	\(0.700004\pi\)
\(3\)	−0.661185	−	0.480379i	−0.381735	−	0.277347i	0.380325	−	0.924853i	\(-0.375812\pi\)
							−0.762060	+	0.647506i	\(0.775812\pi\)
\(5\)	0.441151	+	1.35772i	0.197289	+	0.607192i	0.999942	+	0.0107464i	\(0.00342076\pi\)
							−0.802654	+	0.596445i	\(0.796579\pi\)
\(7\)	−0.446078	−	1.37289i	−0.168602	−	0.518903i	0.830682	−	0.556747i	\(-0.187951\pi\)
							−0.999284	+	0.0378445i	\(0.987951\pi\)
\(11\)	2.53282	−	1.84020i	0.763675	−	0.554843i	−0.136360	−	0.990659i	\(-0.543540\pi\)
							0.900035	+	0.435817i	\(0.143540\pi\)
\(13\)	−3.51081	−	2.55075i	−0.973723	−	0.707451i	−0.0174259	−	0.999848i	\(-0.505547\pi\)
							−0.956297	+	0.292397i	\(0.905547\pi\)
\(17\)	2.29676	−	7.06870i	0.557046	−	1.71441i	−0.133433	−	0.991058i	\(-0.542600\pi\)
							0.690479	−	0.723353i	\(-0.257400\pi\)
\(19\)	2.05110			0.470556			0.235278	−	0.971928i	\(-0.424400\pi\)
							0.235278	+	0.971928i	\(0.424400\pi\)
\(23\)	3.41308			0.711677			0.355839	−	0.934547i	\(-0.384195\pi\)
							0.355839	+	0.934547i	\(0.384195\pi\)
\(29\)	−1.08517	+	0.788423i	−0.201511	+	0.146406i	−0.683965	−	0.729515i	\(-0.739746\pi\)
							0.482453	+	0.875922i	\(0.339746\pi\)
\(31\)	−2.77382	+	8.53693i	−0.498192	+	1.53328i	0.313730	+	0.949512i	\(0.398421\pi\)
							−0.811922	+	0.583766i	\(0.801579\pi\)
\(37\)	−9.15916	−	6.65452i	−1.50576	−	1.09400i	−0.968016	−	0.250887i	\(-0.919278\pi\)
							−0.537741	−	0.843110i	\(-0.680722\pi\)
\(41\)	6.38881	+	4.64174i	0.997765	+	0.724918i	0.961608	−	0.274428i	\(-0.0884884\pi\)
							0.0361569	+	0.999346i	\(0.488488\pi\)
\(43\)	−0.632206	+	1.94573i	−0.0964106	+	0.296721i	−0.987619	−	0.156873i	\(-0.949859\pi\)
							0.891208	+	0.453595i	\(0.149859\pi\)
\(47\)	−2.74280	−	1.99276i	−0.400078	−	0.290674i	0.369495	−	0.929233i	\(-0.379531\pi\)
							−0.769573	+	0.638559i	\(0.779531\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.d.b.59.2	✓	32
151.64	even	5	inner	151.2.d.b.64.2	yes	32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.d.b.59.2	✓	32	1.1	even	1	trivial
151.2.d.b.64.2	yes	32	151.64	even	5	inner