Embedded newform 46.4.c.a.27.2

• Label: 46.4.c.a.27.2
• Level: $46$
• Weight: $4$
• Character: 46.27
• Analytic conductor: $2.714$
• Analytic rank: $0$
• Dimension: $30$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.71408786026\)
Analytic rank:	\(0\)
Dimension:	\(30\)
Relative dimension:	\(3\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			27.2
Character	\(\chi\)	\(=\)	46.27
Dual form			46.4.c.a.29.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.830830 + 1.81926i) q^{2} +(-0.858963 + 0.252214i) q^{3} +(-2.61944 + 3.02300i) q^{4} +(9.50458 + 6.10822i) q^{5} +(-1.17250 - 1.35313i) q^{6} +(3.59878 + 25.0301i) q^{7} +(-7.67594 - 2.25386i) q^{8} +(-22.0396 + 14.1640i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/46\mathbb{Z}\right)^\times\).

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{2}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.830830	+	1.81926i	0.293743	+	0.643207i
							\(3\)	−0.858963	+	0.252214i	−0.165308	+	0.0485387i	−0.363339	−	0.931657i	\(-0.618363\pi\)
0.198031	+	0.980196i	\(0.436545\pi\)
\(5\)	9.50458	+	6.10822i	0.850115	+	0.546336i	0.891611	−	0.452803i	\(-0.149576\pi\)
							−0.0414954	+	0.999139i	\(0.513212\pi\)
\(7\)	3.59878	+	25.0301i	0.194316	+	1.35150i	0.820422	+	0.571758i	\(0.193739\pi\)
							−0.626106	+	0.779738i	\(0.715352\pi\)
\(11\)	26.9613	−	59.0369i	0.739012	−	1.61821i	−0.0461621	−	0.998934i	\(-0.514699\pi\)
							0.785174	−	0.619276i	\(-0.212574\pi\)
\(13\)	3.47253	−	24.1520i	0.0740851	−	0.515273i	−0.918661	−	0.395046i	\(-0.870729\pi\)
							0.992746	−	0.120227i	\(-0.0383623\pi\)
\(17\)	52.5965	+	60.6996i	0.750384	+	0.865989i	0.994605	−	0.103730i	\(-0.0330779\pi\)
							−0.244222	+	0.969719i	\(0.578532\pi\)
\(19\)	94.3889	−	108.931i	1.13970	−	1.31528i	0.197474	−	0.980308i	\(-0.436726\pi\)
							0.942227	−	0.334976i	\(-0.108728\pi\)
\(23\)	−108.786	−	18.2353i	−0.986240	−	0.165318i
							\(29\)	−23.2981	−	26.8874i	−0.149184	−	0.172168i	0.676239	−	0.736683i	\(-0.263609\pi\)
−0.825423	+	0.564515i	\(0.809063\pi\)
\(31\)	−70.4810	−	20.6951i	−0.408347	−	0.119901i	0.0711067	−	0.997469i	\(-0.477347\pi\)
							−0.479454	+	0.877567i	\(0.659165\pi\)
\(37\)	−186.068	+	119.579i	−0.826740	+	0.531313i	−0.884240	−	0.467032i	\(-0.845323\pi\)
							0.0575007	+	0.998345i	\(0.481687\pi\)
\(41\)	251.587	+	161.685i	0.958322	+	0.615876i	0.923533	−	0.383518i	\(-0.125288\pi\)
							0.0347892	+	0.999395i	\(0.488924\pi\)
\(43\)	285.799	−	83.9181i	1.01358	−	0.297614i	0.267563	−	0.963541i	\(-0.413782\pi\)
							0.746017	+	0.665927i	\(0.231964\pi\)
\(47\)	−57.9788			−0.179938			−0.0899689	−	0.995945i	\(-0.528677\pi\)
							−0.0899689	+	0.995945i	\(0.528677\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.a.27.2	✓	30
23.6	even	11	inner	46.4.c.a.29.2	yes	30
23.11	odd	22		1058.4.a.w.1.8		15
23.12	even	11		1058.4.a.v.1.8		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.a.27.2	✓	30	1.1	even	1	trivial
46.4.c.a.29.2	yes	30	23.6	even	11	inner
1058.4.a.v.1.8		15	23.12	even	11
1058.4.a.w.1.8		15	23.11	odd	22