Embedded newform 11.14.c.a.4.3

• Label: 11.14.c.a.4.3
• Level: $11$
• Weight: $14$
• Character: 11.4
• Analytic conductor: $11.795$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.7954021847\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.3
Character	\(\chi\)	\(=\)	11.4
Dual form			11.14.c.a.3.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-97.9783 - 71.1854i) q^{2} +(552.972 - 1701.87i) q^{3} +(2000.91 + 6158.18i) q^{4} +(-26557.7 + 19295.3i) q^{5} +(-175328. + 127383. i) q^{6} +(-163681. - 503758. i) q^{7} +(-64254.1 + 197754. i) q^{8} +(-1.30076e6 - 945060. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 59 q^{2} - 864 q^{3} - 44697 q^{4} - 52240 q^{5} - 130115 q^{6} + 390696 q^{7} + 876527 q^{8} - 3520244 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\)	\(2\)
\(\chi(n)\)	\(e\left(\frac{1}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−97.9783	−	71.1854i	−1.08252	−	0.786495i	−0.104397	−	0.994536i	\(-0.533291\pi\)
							−0.978120	+	0.208041i	\(0.933291\pi\)
\(3\)	552.972	−	1701.87i	0.437941	−	1.34784i	−0.452102	−	0.891966i	\(-0.649326\pi\)
							0.890043	−	0.455877i	\(-0.150674\pi\)
\(5\)	−26557.7	+	19295.3i	−0.760125	+	0.552263i	−0.898949	−	0.438054i	\(-0.855668\pi\)
							0.138823	+	0.990317i	\(0.455668\pi\)
\(7\)	−163681.	−	503758.i	−0.525849	−	1.61840i	−0.762632	−	0.646833i	\(-0.776093\pi\)
							0.236783	−	0.971563i	\(-0.423907\pi\)
\(11\)	−5.33380e6	+	2.46441e6i	−0.907787	+	0.419431i
							\(13\)	9.02711e6	+	6.55858e6i	0.518701	+	0.376858i	0.816114	−	0.577890i	\(-0.196124\pi\)
−0.297413	+	0.954749i	\(0.596124\pi\)
\(17\)	1.10685e8	−	8.04175e7i	1.11217	−	0.808039i	0.129167	−	0.991623i	\(-0.458770\pi\)
							0.983004	+	0.183583i	\(0.0587698\pi\)
\(19\)	−1.71532e7	+	5.27921e7i	−0.0836462	+	0.257437i	−0.984129	−	0.177455i	\(-0.943213\pi\)
							0.900483	+	0.434892i	\(0.143213\pi\)
\(23\)	−9.97174e7			−0.140456			−0.0702279	−	0.997531i	\(-0.522373\pi\)
							−0.0702279	+	0.997531i	\(0.522373\pi\)
\(29\)	9.01971e8	+	2.77598e9i	0.281582	+	0.866622i	0.987402	+	0.158230i	\(0.0505788\pi\)
							−0.705820	+	0.708391i	\(0.749421\pi\)
\(31\)	−6.34578e9	−	4.61048e9i	−1.28420	−	0.933029i	−0.284533	−	0.958666i	\(-0.591838\pi\)
							−0.999671	+	0.0256377i	\(0.991838\pi\)
\(37\)	−8.55959e8	−	2.63437e9i	−0.0548456	−	0.168797i	0.919881	−	0.392197i	\(-0.128285\pi\)
							−0.974727	+	0.223399i	\(0.928285\pi\)
\(41\)	−1.70176e10	+	5.23746e10i	−0.559502	+	1.72197i	0.124244	+	0.992252i	\(0.460350\pi\)
							−0.683746	+	0.729720i	\(0.739650\pi\)
\(43\)	−2.99942e10			−0.723589			−0.361795	−	0.932258i	\(-0.617836\pi\)
							−0.361795	+	0.932258i	\(0.617836\pi\)
\(47\)	−7.78171e9	+	2.39496e10i	−0.105303	+	0.324088i	−0.989801	−	0.142455i	\(-0.954501\pi\)
							0.884499	+	0.466543i	\(0.154501\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.14.c.a.4.3	yes	48
11.3	even	5	inner	11.14.c.a.3.3	✓	48
11.5	even	5		121.14.a.h.1.20		24
11.6	odd	10		121.14.a.i.1.5		24

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.14.c.a.3.3	✓	48	11.3	even	5	inner
11.14.c.a.4.3	yes	48	1.1	even	1	trivial
121.14.a.h.1.20		24	11.5	even	5
121.14.a.i.1.5		24	11.6	odd	10