Embedded newform 43.11.d.a.7.5

• Label: 43.11.d.a.7.5
• Level: $43$
• Weight: $11$
• Character: 43.7
• Analytic conductor: $27.320$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3203618650\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.5
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.32

$q$-expansion

\(f(q)\)	\(=\)	\(q-50.9732i q^{2} +(10.9453 - 6.31925i) q^{3} -1574.27 q^{4} +(3081.80 - 1779.28i) q^{5} +(-322.113 - 557.915i) q^{6} +(5344.72 + 3085.78i) q^{7} +28049.1i q^{8} +(-29444.6 + 50999.6i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	50.9732i		−	1.59291i	−0.604695	−	0.796457i	\(-0.706705\pi\)
							0.604695	−	0.796457i	\(-0.293295\pi\)
\(3\)	10.9453	−	6.31925i	0.0450422	−	0.0260051i	−0.477310	−	0.878735i	\(-0.658388\pi\)
							0.522352	+	0.852730i	\(0.325055\pi\)
\(5\)	3081.80	−	1779.28i	0.986177	−	0.569370i	0.0820476	−	0.996628i	\(-0.473854\pi\)
							0.904129	+	0.427259i	\(0.140521\pi\)
\(7\)	5344.72	+	3085.78i	0.318006	+	0.183601i	0.650503	−	0.759503i	\(-0.274558\pi\)
							−0.332498	+	0.943104i	\(0.607891\pi\)
\(11\)	−187226.			−1.16253			−0.581264	−	0.813715i	\(-0.697442\pi\)
							−0.581264	+	0.813715i	\(0.697442\pi\)
\(13\)	−115284.	+	199678.i	−0.310494	+	0.537792i	−0.978469	−	0.206392i	\(-0.933828\pi\)
							0.667975	+	0.744184i	\(0.267161\pi\)
\(17\)	−668518.	+	1.15791e6i	−0.470835	+	0.815509i	−0.999444	−	0.0333560i	\(-0.989380\pi\)
							0.528609	+	0.848865i	\(0.322714\pi\)
\(19\)	−2.62263e6	+	1.51418e6i	−1.05918	+	0.611518i	−0.925205	−	0.379467i	\(-0.876107\pi\)
							−0.133975	+	0.990985i	\(0.542774\pi\)
\(23\)	−70880.8	−	122769.i	−0.0110126	−	0.0190744i	0.860467	−	0.509507i	\(-0.170172\pi\)
							−0.871479	+	0.490433i	\(0.836839\pi\)
\(29\)	−5.31301e6	−	3.06747e6i	−0.259030	−	0.149551i	0.364862	−	0.931062i	\(-0.381116\pi\)
							−0.623892	+	0.781510i	\(0.714450\pi\)
\(31\)	−1.91289e7	−	3.31322e7i	−0.668161	−	1.15729i	−0.978418	−	0.206635i	\(-0.933749\pi\)
							0.310257	−	0.950653i	\(-0.399585\pi\)
\(37\)	1.03746e8	−	5.98981e7i	1.49611	−	0.863782i	0.496124	−	0.868252i	\(-0.334756\pi\)
							0.999990	+	0.00446952i	\(0.00142270\pi\)
\(41\)	−2.68172e7			−0.231470			−0.115735	−	0.993280i	\(-0.536922\pi\)
							−0.115735	+	0.993280i	\(0.536922\pi\)
\(43\)	1.01261e8	+	1.06572e8i	0.688812	+	0.724940i
							\(47\)	−2.46853e8			−1.07634			−0.538169	−	0.842837i	\(-0.680884\pi\)
−0.538169	+	0.842837i	\(0.680884\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.5	✓	72
43.37	odd	6	inner	43.11.d.a.37.32	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.5	✓	72	1.1	even	1	trivial
43.11.d.a.37.32	yes	72	43.37	odd	6	inner