Embedded newform 43.4.g.a.24.10

• Label: 43.4.g.a.24.10
• Level: $43$
• Weight: $4$
• Character: 43.24
• Analytic conductor: $2.537$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.53708213025\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(10\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.10
Character	\(\chi\)	\(=\)	43.24
Dual form			43.4.g.a.9.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(3.27326 - 4.10454i) q^{2} +(-9.59032 + 1.44551i) q^{3} +(-4.35283 - 19.0710i) q^{4} +(4.62627 - 3.15414i) q^{5} +(-25.4585 + 44.0953i) q^{6} +(0.410104 + 0.710321i) q^{7} +(-54.6855 - 26.3351i) q^{8} +(64.0843 - 19.7674i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{20}{21}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.27326	−	4.10454i	1.15727	−	1.45117i	0.287457	−	0.957794i	\(-0.407190\pi\)
							0.869815	−	0.493379i	\(-0.164238\pi\)
\(3\)	−9.59032	+	1.44551i	−1.84566	+	0.278188i	−0.976368	−	0.216114i	\(-0.930662\pi\)
							−0.869290	+	0.494302i	\(0.835424\pi\)
\(5\)	4.62627	−	3.15414i	0.413786	−	0.282115i	−0.338480	−	0.940973i	\(-0.609913\pi\)
							0.752267	+	0.658859i	\(0.228960\pi\)
\(7\)	0.410104	+	0.710321i	0.0221435	+	0.0383537i	0.876885	−	0.480701i	\(-0.159618\pi\)
							−0.854741	+	0.519054i	\(0.826284\pi\)
\(11\)	10.7845	−	47.2502i	0.295606	−	1.29513i	−0.580992	−	0.813909i	\(-0.697335\pi\)
							0.876598	−	0.481224i	\(-0.159808\pi\)
\(13\)	0.341528	+	4.55738i	0.00728637	+	0.0972299i	0.999661	−	0.0260263i	\(-0.00828536\pi\)
							−0.992375	+	0.123256i	\(0.960666\pi\)
\(17\)	89.5805	+	61.0749i	1.27803	+	0.871344i	0.996112	−	0.0880955i	\(-0.0280781\pi\)
							0.281915	+	0.959439i	\(0.409030\pi\)
\(19\)	−23.1028	−	7.12628i	−0.278956	−	0.0860464i	0.152121	−	0.988362i	\(-0.451390\pi\)
							−0.431076	+	0.902316i	\(0.641866\pi\)
\(23\)	0.872249	+	0.809328i	0.00790767	+	0.00733725i	0.684117	−	0.729373i	\(-0.260188\pi\)
							−0.676209	+	0.736710i	\(0.736378\pi\)
\(29\)	31.9017	+	4.80840i	0.204275	+	0.0307896i	0.250383	−	0.968147i	\(-0.419444\pi\)
							−0.0461073	+	0.998936i	\(0.514682\pi\)
\(31\)	−21.6187	−	55.0835i	−0.125253	−	0.319138i	0.854469	−	0.519502i	\(-0.173883\pi\)
							−0.979721	+	0.200364i	\(0.935787\pi\)
\(37\)	176.750	−	306.141i	0.785340	−	1.36025i	−0.143456	−	0.989657i	\(-0.545821\pi\)
							0.928796	−	0.370592i	\(-0.120845\pi\)
\(41\)	−39.1724	+	49.1207i	−0.149212	+	0.187106i	−0.850820	−	0.525457i	\(-0.823894\pi\)
							0.701608	+	0.712563i	\(0.252466\pi\)
\(43\)	94.5222	+	265.655i	0.335221	+	0.942140i
							\(47\)	47.4520	+	207.901i	0.147268	+	0.645223i	0.993637	+	0.112627i	\(0.0359264\pi\)
−0.846370	+	0.532596i	\(0.821216\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.g.a.24.10	yes	120
43.3	odd	42		1849.4.a.k.1.5		60
43.9	even	21	inner	43.4.g.a.9.10	✓	120
43.40	even	21		1849.4.a.l.1.56		60

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.9.10	✓	120	43.9	even	21	inner
43.4.g.a.24.10	yes	120	1.1	even	1	trivial
1849.4.a.k.1.5		60	43.3	odd	42
1849.4.a.l.1.56		60	43.40	even	21