Embedded newform 43.7.h.a.18.11

• Label: 43.7.h.a.18.11
• 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			18.11
Character	\(\chi\)	\(=\)	43.18
Dual form			43.7.h.a.12.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.758988 - 1.57606i) q^{2} +(6.18403 - 9.07030i) q^{3} +(37.9955 + 47.6448i) q^{4} +(-99.6397 - 107.386i) q^{5} +(-9.60169 - 16.6306i) q^{6} +(-494.102 - 285.270i) q^{7} +(213.077 - 48.6333i) q^{8} +(222.305 + 566.425i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.758988	−	1.57606i	0.0948735	−	0.197007i	−0.848131	−	0.529786i	\(-0.822272\pi\)
							0.943005	+	0.332779i	\(0.107986\pi\)
\(3\)	6.18403	−	9.07030i	0.229038	−	0.335937i	−0.694466	−	0.719525i	\(-0.744359\pi\)
							0.923504	+	0.383588i	\(0.125312\pi\)
\(5\)	−99.6397	−	107.386i	−0.797117	−	0.859088i	0.195459	−	0.980712i	\(-0.437380\pi\)
							−0.992576	+	0.121624i	\(0.961190\pi\)
\(7\)	−494.102	−	285.270i	−1.44053	−	0.831691i	−0.442645	−	0.896697i	\(-0.645960\pi\)
							−0.997885	+	0.0650062i	\(0.979293\pi\)
\(11\)	1481.81	−	1858.14i	1.11331	−	1.39604i	0.204482	−	0.978870i	\(-0.434449\pi\)
							0.908827	−	0.417174i	\(-0.136979\pi\)
\(13\)	−3550.76	−	1095.26i	−1.61619	−	0.498527i	−0.650777	−	0.759269i	\(-0.725557\pi\)
							−0.965409	+	0.260741i	\(0.916033\pi\)
\(17\)	−5513.15	−	5115.45i	−1.12215	−	1.04121i	−0.998806	−	0.0488442i	\(-0.984446\pi\)
							−0.123348	−	0.992363i	\(-0.539363\pi\)
\(19\)	−789.362	−	309.802i	−0.115084	−	0.0451672i	0.307100	−	0.951677i	\(-0.400641\pi\)
							−0.422184	+	0.906510i	\(0.638737\pi\)
\(23\)	789.621	+	119.016i	0.0648986	+	0.00978189i	0.181411	−	0.983407i	\(-0.441933\pi\)
							−0.116513	+	0.993189i	\(0.537172\pi\)
\(29\)	10248.1	+	15031.2i	0.420195	+	0.616312i	0.976720	−	0.214518i	\(-0.0688181\pi\)
							−0.556525	+	0.830831i	\(0.687866\pi\)
\(31\)	11.1854	+	149.259i	0.000375464	+	0.00501022i	0.997388	−	0.0722247i	\(-0.0230099\pi\)
							−0.997013	+	0.0772350i	\(0.975391\pi\)
\(37\)	45473.4	−	26254.1i	0.897744	−	0.518313i	0.0212764	−	0.999774i	\(-0.493227\pi\)
							0.876468	+	0.481461i	\(0.159894\pi\)
\(41\)	−35500.2	−	17096.0i	−0.515086	−	0.248052i	0.158237	−	0.987401i	\(-0.449419\pi\)
							−0.673322	+	0.739349i	\(0.735133\pi\)
\(43\)	68072.6	−	41079.0i	0.856184	−	0.516671i
							\(47\)	89983.6	+	112836.i	0.866702	+	1.08681i	0.995464	+	0.0951345i	\(0.0303281\pi\)
−0.128762	+	0.991675i	\(0.541100\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.h.a.18.11	yes	252
43.12	odd	42	inner	43.7.h.a.12.11	✓	252

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.h.a.12.11	✓	252	43.12	odd	42	inner
43.7.h.a.18.11	yes	252	1.1	even	1	trivial