Embedded newform 43.7.h.a.19.14

• Label: 43.7.h.a.19.14
• Level: $43$
• Weight: $7$
• Character: 43.19
• 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			19.14
Character	\(\chi\)	\(=\)	43.19
Dual form			43.7.h.a.34.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(4.10621 + 3.27459i) q^{2} +(-3.10406 - 20.5941i) q^{3} +(-8.10334 - 35.5031i) q^{4} +(95.1661 + 139.583i) q^{5} +(54.6913 - 94.7280i) q^{6} +(-111.394 + 64.3135i) q^{7} +(228.826 - 475.161i) q^{8} +(282.132 - 87.0263i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{19}{42}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.10621	+	3.27459i	0.513276	+	0.409324i	0.845580	−	0.533848i	\(-0.179255\pi\)
							−0.332304	+	0.943172i	\(0.607826\pi\)
\(3\)	−3.10406	−	20.5941i	−0.114965	−	0.762743i	−0.969810	−	0.243860i	\(-0.921586\pi\)
							0.854845	−	0.518883i	\(-0.173652\pi\)
\(5\)	95.1661	+	139.583i	0.761329	+	1.11666i	0.989709	+	0.143092i	\(0.0457045\pi\)
							−0.228381	+	0.973572i	\(0.573343\pi\)
\(7\)	−111.394	+	64.3135i	−0.324765	+	0.187503i	−0.653514	−	0.756914i	\(-0.726706\pi\)
							0.328750	+	0.944417i	\(0.393373\pi\)
\(11\)	502.836	−	2203.07i	0.377788	−	1.65520i	−0.326436	−	0.945219i	\(-0.605848\pi\)
							0.704224	−	0.709978i	\(-0.251295\pi\)
\(13\)	−305.469	−	4076.20i	−0.139039	−	1.85535i	−0.435354	−	0.900259i	\(-0.643377\pi\)
							0.296315	−	0.955090i	\(-0.404242\pi\)
\(17\)	4033.57	+	2750.04i	0.820999	+	0.559748i	0.899376	−	0.437176i	\(-0.144021\pi\)
							−0.0783766	+	0.996924i	\(0.524974\pi\)
\(19\)	−2866.15	+	9291.84i	−0.417867	+	1.35469i	0.465100	+	0.885258i	\(0.346018\pi\)
							−0.882967	+	0.469435i	\(0.844458\pi\)
\(23\)	2093.72	+	1942.68i	0.172081	+	0.159668i	0.761512	−	0.648151i	\(-0.224457\pi\)
							−0.589431	+	0.807819i	\(0.700648\pi\)
\(29\)	−779.707	+	5173.02i	−0.0319696	+	0.212104i	−0.999112	−	0.0421304i	\(-0.986586\pi\)
							0.967143	+	0.254235i	\(0.0818236\pi\)
\(31\)	1861.07	+	4741.94i	0.0624710	+	0.159174i	0.958701	−	0.284417i	\(-0.0917999\pi\)
							−0.896230	+	0.443590i	\(0.853705\pi\)
\(37\)	81657.5	+	47145.0i	1.61210	+	0.930744i	0.988884	+	0.148692i	\(0.0475063\pi\)
							0.623213	+	0.782052i	\(0.285827\pi\)
\(41\)	24975.6	−	31318.4i	0.362380	−	0.454410i	−0.566900	−	0.823787i	\(-0.691857\pi\)
							0.929280	+	0.369377i	\(0.120429\pi\)
\(43\)	−39413.7	+	69050.1i	−0.495727	+	0.868479i
							\(47\)	−19584.2	−	85803.9i	−0.188630	−	0.826444i	−0.977340	−	0.211677i	\(-0.932107\pi\)
0.788709	−	0.614766i	\(-0.210750\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.h.a.19.14	✓	252
43.34	odd	42	inner	43.7.h.a.34.14	yes	252

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.h.a.19.14	✓	252	1.1	even	1	trivial
43.7.h.a.34.14	yes	252	43.34	odd	42	inner