Newform orbit 92.4.e.a

• Label: 92.4.e.a
• Level: $92$
• Weight: $4$
• Character orbit: 92.e
• Analytic conductor: $5.428$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.42817572053\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(6\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 4 q^{3} + 10 q^{5} + 4 q^{7} - 50 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−5.94812	−	6.86450i		0		−2.47285	−	17.1990i		0		−9.94416	+	21.7747i		0		−7.89869	+	54.9366i		0
9.2		0		−4.30440	−	4.96755i		0		2.74874	+	19.1179i		0		2.80895	−	6.15073i		0		−2.30613	+	16.0395i		0
9.3		0		−2.03078	−	2.34364i		0		0.0528208	+	0.367377i		0		2.56731	−	5.62162i		0		2.47390	−	17.2063i		0
9.4		0		1.94743	+	2.24745i		0		−1.75467	−	12.2040i		0		6.07696	−	13.3067i		0		2.58393	−	17.9717i		0
9.5		0		2.73530	+	3.15670i		0		0.728959	+	5.07002i		0		−12.1640	+	26.6355i		0		1.35959	−	9.45615i		0
9.6		0		6.51242	+	7.51573i		0		1.77332	+	12.3337i		0		10.8914	−	23.8489i		0		−10.2321	+	71.1661i		0
13.1		0		−7.73296	−	4.96967i		0		3.29460	−	7.21417i		0		−7.27376	−	2.13577i		0		23.8848	+	52.3005i		0
13.2		0		−3.98530	−	2.56119i		0		−3.66438	+	8.02386i		0		26.9581	+	7.91560i		0		−1.89333	−	4.14582i		0
13.3		0		−1.63982	−	1.05385i		0		1.29648	−	2.83889i		0		−10.8736	−	3.19277i		0		−9.63779	−	21.1038i		0
13.4		0		0.898651	+	0.577528i		0		−6.80968	+	14.9111i		0		−16.3833	−	4.81056i		0		−10.7422	−	23.5221i		0
13.5		0		2.46918	+	1.58684i		0		7.80656	−	17.0940i		0		−4.36661	−	1.28215i		0		−7.63745	−	16.7237i		0
13.6		0		6.76154	+	4.34538i		0		−1.10567	+	2.42107i		0		13.5335	+	3.97379i		0		15.6199	+	34.2029i		0
25.1		0		−1.14976	−	7.99674i		0		20.3141	+	5.96476i		0		5.26860	−	6.08029i		0		−36.7197	+	10.7819i		0
25.2		0		−0.892386	−	6.20668i		0		−10.3452	−	3.03763i		0		−4.40029	+	5.07821i		0		−11.8202	+	3.47074i		0
25.3		0		−0.00313457	−	0.0218014i		0		−2.96928	−	0.871860i		0		10.9723	−	12.6627i		0		25.9058	−	7.60664i		0
25.4		0		0.155250	+	1.07979i		0		9.05574	+	2.65901i		0		−22.7662	+	26.2736i		0		24.7645	−	7.27151i		0
25.5		0		1.13079	+	7.86481i		0		−14.8990	−	4.37475i		0		−5.89997	+	6.80893i		0		−34.6703	+	10.1801i		0
25.6		0		1.13203	+	7.87341i		0		15.9884	+	4.69462i		0		14.3122	−	16.5172i		0		−34.8028	+	10.2190i		0
29.1		0		−9.54355	−	2.80224i		0		−5.07470	+	3.26131i		0		1.87377	−	13.0324i		0		60.5130	+	38.8894i		0
29.2		0		−3.39304	−	0.996287i		0		7.40132	−	4.75654i		0		−0.533135	+	3.70804i		0		−12.1937	−	7.83642i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.4.e.a	✓	60
23.c	even	11	1	inner	92.4.e.a	✓	60
23.c	even	11	1		2116.4.a.i		30
23.d	odd	22	1		2116.4.a.j		30

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.4.e.a	✓	60	1.a	even	1	1	trivial
92.4.e.a	✓	60	23.c	even	11	1	inner
2116.4.a.i		30	23.c	even	11	1
2116.4.a.j		30	23.d	odd	22	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(92, [\chi])\).