Embedded newform 43.7.h.a.18.14

• Label: 43.7.h.a.18.14
• 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			18.14
Character	\(\chi\)	\(=\)	43.18
Dual form			43.7.h.a.12.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.71537 - 5.63853i) q^{2} +(26.7438 - 39.2259i) q^{3} +(15.4836 + 19.4158i) q^{4} +(-88.5928 - 95.4804i) q^{5} +(-148.557 - 257.309i) q^{6} +(-56.9713 - 32.8924i) q^{7} +(542.009 - 123.710i) q^{8} +(-557.109 - 1419.49i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.71537	−	5.63853i	0.339422	−	0.704817i	−0.659477	−	0.751724i	\(-0.729222\pi\)
							0.998899	+	0.0469078i	\(0.0149367\pi\)
\(3\)	26.7438	−	39.2259i	0.990510	−	1.45281i	0.101548	−	0.994831i	\(-0.467620\pi\)
							0.888962	−	0.457981i	\(-0.151427\pi\)
\(5\)	−88.5928	−	95.4804i	−0.708743	−	0.763843i	0.271329	−	0.962487i	\(-0.412537\pi\)
							−0.980072	+	0.198644i	\(0.936346\pi\)
\(7\)	−56.9713	−	32.8924i	−0.166097	−	0.0958962i	0.414647	−	0.909982i	\(-0.363905\pi\)
							−0.580744	+	0.814086i	\(0.697238\pi\)
\(11\)	−698.868	+	876.353i	−0.525070	+	0.658417i	−0.971677	−	0.236313i	\(-0.924061\pi\)
							0.446607	+	0.894730i	\(0.352632\pi\)
\(13\)	2664.69	+	821.948i	1.21288	+	0.374123i	0.834229	−	0.551418i	\(-0.185913\pi\)
							0.378648	+	0.925541i	\(0.376389\pi\)
\(17\)	573.969	+	532.566i	0.116827	+	0.108399i	0.736423	−	0.676521i	\(-0.236513\pi\)
							−0.619597	+	0.784920i	\(0.712704\pi\)
\(19\)	−8774.55	−	3443.76i	−1.27928	−	0.502078i	−0.374207	−	0.927345i	\(-0.622085\pi\)
							−0.905068	+	0.425267i	\(0.860180\pi\)
\(23\)	13600.0	+	2049.88i	1.11778	+	0.168478i	0.681843	−	0.731498i	\(-0.261179\pi\)
							0.435938	+	0.899977i	\(0.356417\pi\)
\(29\)	2791.31	+	4094.11i	0.114450	+	0.167867i	0.879189	−	0.476472i	\(-0.158085\pi\)
							−0.764740	+	0.644339i	\(0.777132\pi\)
\(31\)	149.682	+	1997.37i	0.00502441	+	0.0670461i	0.999152	−	0.0411648i	\(-0.0131069\pi\)
							−0.994128	+	0.108211i	\(0.965488\pi\)
\(37\)	6756.33	−	3900.77i	0.133385	−	0.0770096i	−0.431823	−	0.901958i	\(-0.642129\pi\)
							0.565207	+	0.824949i	\(0.308796\pi\)
\(41\)	83404.6	+	40165.5i	1.21015	+	0.582776i	0.926552	−	0.376168i	\(-0.122758\pi\)
							0.283596	+	0.958944i	\(0.408473\pi\)
\(43\)	71359.7	−	35059.4i	0.897527	−	0.440960i
							\(47\)	47685.4	+	59795.6i	0.459295	+	0.575938i	0.956514	−	0.291688i	\(-0.0942167\pi\)
−0.497219	+	0.867625i	\(0.665645\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.h.a.18.14	yes	252
43.12	odd	42	inner	43.7.h.a.12.14	✓	252

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.h.a.12.14	✓	252	43.12	odd	42	inner
43.7.h.a.18.14	yes	252	1.1	even	1	trivial