Embedded newform 151.2.h.a.84.11

• Label: 151.2.h.a.84.11
• Level: $151$
• Weight: $2$
• Character: 151.84
• 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			84.11
Character	\(\chi\)	\(=\)	151.84
Dual form			151.2.h.a.9.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.849962 + 2.61591i) q^{2} +(0.0476841 - 0.757917i) q^{3} +(-4.50253 + 3.27128i) q^{4} +(1.44306 + 0.182301i) q^{5} +(2.02318 - 0.519463i) q^{6} +(-1.39396 + 2.96231i) q^{7} +(-7.93392 - 5.76433i) q^{8} +(2.40418 + 0.303718i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{23}{25}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.849962	+	2.61591i	0.601014	+	1.84973i	0.522167	+	0.852843i	\(0.325124\pi\)
							0.0788472	+	0.996887i	\(0.474876\pi\)
\(3\)	0.0476841	−	0.757917i	0.0275304	−	0.437584i	−0.959984	−	0.280055i	\(-0.909647\pi\)
							0.987514	−	0.157529i	\(-0.0503527\pi\)
\(5\)	1.44306	+	0.182301i	0.645356	+	0.0815275i	0.441197	−	0.897410i	\(-0.354554\pi\)
							0.204159	+	0.978938i	\(0.434554\pi\)
\(7\)	−1.39396	+	2.96231i	−0.526866	+	1.11965i	0.447418	+	0.894325i	\(0.352344\pi\)
							−0.974284	+	0.225323i	\(0.927656\pi\)
\(11\)	−0.289014	−	4.59375i	−0.0871411	−	1.38507i	−0.762218	−	0.647321i	\(-0.775889\pi\)
							0.675077	−	0.737748i	\(-0.264111\pi\)
\(13\)	−0.448952	+	0.542689i	−0.124517	+	0.150515i	−0.829088	−	0.559119i	\(-0.811140\pi\)
							0.704571	+	0.709634i	\(0.251140\pi\)
\(17\)	2.16701	+	4.60514i	0.525578	+	1.11691i	0.974716	+	0.223448i	\(0.0717312\pi\)
							−0.449138	+	0.893462i	\(0.648269\pi\)
\(19\)	4.59021	−	3.33498i	1.05307	−	0.765097i	0.0802728	−	0.996773i	\(-0.474421\pi\)
							0.972793	+	0.231676i	\(0.0744208\pi\)
\(23\)	2.09019	−	1.51861i	0.435835	−	0.316653i	−0.348143	−	0.937441i	\(-0.613188\pi\)
							0.783978	+	0.620789i	\(0.213188\pi\)
\(29\)	3.50602	−	1.38813i	0.651051	−	0.257769i	−0.0192995	−	0.999814i	\(-0.506144\pi\)
							0.670351	+	0.742044i	\(0.266144\pi\)
\(31\)	−0.950032	+	0.892139i	−0.170631	+	0.160233i	−0.765158	−	0.643842i	\(-0.777339\pi\)
							0.594527	+	0.804075i	\(0.297339\pi\)
\(37\)	−3.74778	+	4.53029i	−0.616131	+	0.744775i	−0.982616	−	0.185649i	\(-0.940561\pi\)
							0.366485	+	0.930424i	\(0.380561\pi\)
\(41\)	−3.44747	+	0.885160i	−0.538405	+	0.138239i	−0.508094	−	0.861302i	\(-0.669650\pi\)
							−0.0303108	+	0.999541i	\(0.509650\pi\)
\(43\)	−2.95715	−	6.28425i	−0.450960	−	0.958340i	−0.993014	−	0.117996i	\(-0.962353\pi\)
							0.542054	−	0.840344i	\(-0.317647\pi\)
\(47\)	−7.93146	+	2.03645i	−1.15692	+	0.297047i	−0.777929	−	0.628352i	\(-0.783730\pi\)
							−0.378993	+	0.925399i	\(0.623730\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.h.a.84.11	yes	220
151.9	even	25	inner	151.2.h.a.9.11	✓	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.h.a.9.11	✓	220	151.9	even	25	inner
151.2.h.a.84.11	yes	220	1.1	even	1	trivial