Embedded newform 151.2.g.a.2.5

• Label: 151.2.g.a.2.5
• Level: $151$
• Weight: $2$
• Character: 151.2
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $96$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(12\) over \(\Q(\zeta_{15})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			2.5
Character	\(\chi\)	\(=\)	151.2
Dual form			151.2.g.a.76.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.465766 + 0.806731i) q^{2} +(-2.42147 + 1.75930i) q^{3} +(0.566123 + 0.980554i) q^{4} +(1.07846 + 1.19776i) q^{5} +(-0.291444 - 2.77290i) q^{6} +(-0.384809 - 0.427373i) q^{7} -2.91779 q^{8} +(1.84134 - 5.66705i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{7}{15}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.465766	+	0.806731i	−0.329347	+	0.570445i	−0.982382	−	0.186882i	\(-0.940162\pi\)
							0.653036	+	0.757327i	\(0.273495\pi\)
\(3\)	−2.42147	+	1.75930i	−1.39804	+	1.01573i	−0.403110	+	0.915152i	\(0.632071\pi\)
							−0.994929	+	0.100583i	\(0.967929\pi\)
\(5\)	1.07846	+	1.19776i	0.482304	+	0.535653i	0.934357	−	0.356338i	\(-0.115975\pi\)
							−0.452053	+	0.891991i	\(0.649308\pi\)
\(7\)	−0.384809	−	0.427373i	−0.145444	−	0.161532i	0.666021	−	0.745933i	\(-0.267996\pi\)
							−0.811465	+	0.584401i	\(0.801329\pi\)
\(11\)	−1.96090	+	0.873048i	−0.591233	+	0.263234i	−0.680469	−	0.732777i	\(-0.738224\pi\)
							0.0892363	+	0.996010i	\(0.471557\pi\)
\(13\)	−0.715073	−	0.318371i	−0.198326	−	0.0883002i	0.305171	−	0.952298i	\(-0.401287\pi\)
							−0.503496	+	0.863997i	\(0.667953\pi\)
\(17\)	2.30510	+	0.489965i	0.559069	+	0.118834i	0.478776	−	0.877937i	\(-0.341081\pi\)
							0.0802939	+	0.996771i	\(0.474414\pi\)
\(19\)	1.37182			0.314716			0.157358	−	0.987542i	\(-0.449702\pi\)
							0.157358	+	0.987542i	\(0.449702\pi\)
\(23\)	−3.95119	+	6.84365i	−0.823879	+	1.42700i	0.0788939	+	0.996883i	\(0.474861\pi\)
							−0.902773	+	0.430117i	\(0.858472\pi\)
\(29\)	3.76386	+	2.73461i	0.698932	+	0.507804i	0.879584	−	0.475743i	\(-0.157821\pi\)
							−0.180652	+	0.983547i	\(0.557821\pi\)
\(31\)	8.86672	+	1.88468i	1.59251	+	0.338499i	0.917011	−	0.398862i	\(-0.130595\pi\)
							0.675500	+	0.737360i	\(0.263928\pi\)
\(37\)	0.862247	+	8.20374i	0.141753	+	1.34869i	0.801859	+	0.597514i	\(0.203845\pi\)
							−0.660106	+	0.751172i	\(0.729489\pi\)
\(41\)	−9.49425	+	6.89797i	−1.48275	+	1.07728i	−0.506095	+	0.862477i	\(0.668912\pi\)
							−0.976657	+	0.214805i	\(0.931088\pi\)
\(43\)	−1.99664	+	2.21750i	−0.304485	+	0.338165i	−0.875897	−	0.482499i	\(-0.839729\pi\)
							0.571412	+	0.820664i	\(0.306396\pi\)
\(47\)	−8.66953	−	3.85992i	−1.26458	−	0.563027i	−0.338718	−	0.940888i	\(-0.609993\pi\)
							−0.925862	+	0.377861i	\(0.876660\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.g.a.2.5	✓	96
151.76	even	15	inner	151.2.g.a.76.5	yes	96

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.g.a.2.5	✓	96	1.1	even	1	trivial
151.2.g.a.76.5	yes	96	151.76	even	15	inner