Embedded newform 43.7.h.a.18.10

• Label: 43.7.h.a.18.10
• Level: $43$
• Weight: $7$
• Character: 43.18
• Analytic conductor: $9.892$
• Analytic rank: $0$
• Dimension: $252$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.h (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.89232559565\)
Analytic rank:	\(0\)
Dimension:	\(252\)
Relative dimension:	\(21\) over \(\Q(\zeta_{42})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			18.10
Character	\(\chi\)	\(=\)	43.18
Dual form			43.7.h.a.12.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.799977 + 1.66117i) q^{2} +(12.6741 - 18.5895i) q^{3} +(37.7838 + 47.3794i) q^{4} +(102.613 + 110.590i) q^{5} +(20.7413 + 35.9249i) q^{6} +(-237.876 - 137.338i) q^{7} +(-223.973 + 51.1205i) q^{8} +(81.3979 + 207.398i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{29}{42}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.799977	+	1.66117i	−0.0999971	+	0.207646i	−0.944965	−	0.327170i	\(-0.893905\pi\)
							0.844968	+	0.534816i	\(0.179619\pi\)
\(3\)	12.6741	−	18.5895i	0.469410	−	0.688499i	−0.516403	−	0.856346i	\(-0.672729\pi\)
							0.985813	+	0.167847i	\(0.0536816\pi\)
\(5\)	102.613	+	110.590i	0.820902	+	0.884722i	0.994987	−	0.100009i	\(-0.0318870\pi\)
							−0.174084	+	0.984731i	\(0.555697\pi\)
\(7\)	−237.876	−	137.338i	−0.693516	−	0.400402i	0.111412	−	0.993774i	\(-0.464463\pi\)
							−0.804928	+	0.593372i	\(0.797796\pi\)
\(11\)	−158.530	+	198.791i	−0.119106	+	0.149354i	−0.837810	−	0.545962i	\(-0.816164\pi\)
							0.718704	+	0.695316i	\(0.244736\pi\)
\(13\)	2083.61	+	642.708i	0.948388	+	0.292539i	0.730096	−	0.683344i	\(-0.239475\pi\)
							0.218292	+	0.975883i	\(0.429951\pi\)
\(17\)	2499.01	+	2318.74i	0.508652	+	0.471960i	0.892251	−	0.451540i	\(-0.149125\pi\)
							−0.383599	+	0.923500i	\(0.625316\pi\)
\(19\)	−937.665	−	368.006i	−0.136706	−	0.0536531i	0.296002	−	0.955187i	\(-0.404347\pi\)
							−0.432708	+	0.901534i	\(0.642442\pi\)
\(23\)	6916.02	+	1042.42i	0.568425	+	0.0856762i	0.426966	−	0.904268i	\(-0.359583\pi\)
							0.141459	+	0.989944i	\(0.454821\pi\)
\(29\)	2497.16	+	3662.66i	0.102389	+	0.150177i	0.874014	−	0.485901i	\(-0.161508\pi\)
							−0.771625	+	0.636077i	\(0.780556\pi\)
\(31\)	−3526.55	−	47058.6i	−0.118376	−	1.57962i	−0.667967	−	0.744191i	\(-0.732835\pi\)
							0.549591	−	0.835434i	\(-0.314784\pi\)
\(37\)	2704.52	−	1561.46i	0.0533932	−	0.0308266i	−0.473066	−	0.881027i	\(-0.656853\pi\)
							0.526459	+	0.850201i	\(0.323519\pi\)
\(41\)	−30863.0	−	14862.8i	−0.447802	−	0.215650i	0.196371	−	0.980530i	\(-0.437084\pi\)
							−0.644173	+	0.764879i	\(0.722799\pi\)
\(43\)	−57593.4	+	54812.1i	−0.724381	+	0.689400i
							\(47\)	−81619.3	−	102347.i	−0.786139	−	0.985787i	−0.999960	−	0.00891411i	\(-0.997163\pi\)
0.213821	−	0.976873i	\(-0.431409\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.h.a.18.10	yes	252
43.12	odd	42	inner	43.7.h.a.12.10	✓	252

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.h.a.12.10	✓	252	43.12	odd	42	inner
43.7.h.a.18.10	yes	252	1.1	even	1	trivial