Newform orbit 200.3.i.c

• Label: 200.3.i.c
• Level: $200$
• Weight: $3$
• Character orbit: 200.i
• Analytic conductor: $5.450$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.44960528721\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 36 q^{6} + 124 q^{16} - 120 q^{26} + 256 q^{31} - 48 q^{36} - 96 q^{41} - 16 q^{46} - 120 q^{56} - 276 q^{66} - 768 q^{71} - 420 q^{76} - 576 q^{81} + 72 q^{86} + 1164 q^{96}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
93.1	−1.99262	−	0.171617i	−3.89304	+	3.89304i	3.94109	+	0.683938i		0		8.42547	−	7.08924i	5.35873	−	5.35873i	−7.73574	−	2.03919i		−	21.3115i		0
93.2	−1.96516	+	0.371680i	2.03113	−	2.03113i	3.72371	−	1.46082i		0		−3.23656	+	4.74642i	−8.18149	+	8.18149i	−6.77472	+	4.25478i			0.749053i		0
93.3	−1.87738	+	0.689531i	−1.90119	+	1.90119i	3.04909	−	2.58902i		0		2.25832	−	4.88017i	0.633530	−	0.633530i	−3.93909	+	6.96301i			1.77098i		0
93.4	−1.58541	−	1.21921i	1.05085	−	1.05085i	1.02703	+	3.86590i		0		−2.94723	+	0.384812i	−3.45629	+	3.45629i	3.08510	−	7.38120i			6.79144i		0
93.5	−1.21921	−	1.58541i	1.05085	−	1.05085i	−1.02703	+	3.86590i		0		−2.94723	−	0.384812i	3.45629	−	3.45629i	7.38120	−	3.08510i			6.79144i		0
93.6	−0.689531	+	1.87738i	1.90119	−	1.90119i	−3.04909	−	2.58902i		0		2.25832	+	4.88017i	0.633530	−	0.633530i	6.96301	−	3.93909i			1.77098i		0
93.7	−0.371680	+	1.96516i	−2.03113	+	2.03113i	−3.72371	−	1.46082i		0		−3.23656	−	4.74642i	−8.18149	+	8.18149i	4.25478	−	6.77472i			0.749053i		0
93.8	−0.171617	−	1.99262i	−3.89304	+	3.89304i	−3.94109	+	0.683938i		0		8.42547	+	7.08924i	−5.35873	+	5.35873i	2.03919	+	7.73574i		−	21.3115i		0
93.9	0.171617	+	1.99262i	3.89304	−	3.89304i	−3.94109	+	0.683938i		0		8.42547	+	7.08924i	5.35873	−	5.35873i	−2.03919	−	7.73574i		−	21.3115i		0
93.10	0.371680	−	1.96516i	2.03113	−	2.03113i	−3.72371	−	1.46082i		0		−3.23656	−	4.74642i	8.18149	−	8.18149i	−4.25478	+	6.77472i			0.749053i		0
93.11	0.689531	−	1.87738i	−1.90119	+	1.90119i	−3.04909	−	2.58902i		0		2.25832	+	4.88017i	−0.633530	+	0.633530i	−6.96301	+	3.93909i			1.77098i		0
93.12	1.21921	+	1.58541i	−1.05085	+	1.05085i	−1.02703	+	3.86590i		0		−2.94723	−	0.384812i	−3.45629	+	3.45629i	−7.38120	+	3.08510i			6.79144i		0
93.13	1.58541	+	1.21921i	−1.05085	+	1.05085i	1.02703	+	3.86590i		0		−2.94723	+	0.384812i	3.45629	−	3.45629i	−3.08510	+	7.38120i			6.79144i		0
93.14	1.87738	−	0.689531i	1.90119	−	1.90119i	3.04909	−	2.58902i		0		2.25832	−	4.88017i	−0.633530	+	0.633530i	3.93909	−	6.96301i			1.77098i		0
93.15	1.96516	−	0.371680i	−2.03113	+	2.03113i	3.72371	−	1.46082i		0		−3.23656	+	4.74642i	8.18149	−	8.18149i	6.77472	−	4.25478i			0.749053i		0
93.16	1.99262	+	0.171617i	3.89304	−	3.89304i	3.94109	+	0.683938i		0		8.42547	−	7.08924i	−5.35873	+	5.35873i	7.73574	+	2.03919i		−	21.3115i		0
157.1	−1.99262	+	0.171617i	−3.89304	−	3.89304i	3.94109	−	0.683938i		0		8.42547	+	7.08924i	5.35873	+	5.35873i	−7.73574	+	2.03919i			21.3115i		0
157.2	−1.96516	−	0.371680i	2.03113	+	2.03113i	3.72371	+	1.46082i		0		−3.23656	−	4.74642i	−8.18149	−	8.18149i	−6.77472	−	4.25478i		−	0.749053i		0
157.3	−1.87738	−	0.689531i	−1.90119	−	1.90119i	3.04909	+	2.58902i		0		2.25832	+	4.88017i	0.633530	+	0.633530i	−3.93909	−	6.96301i		−	1.77098i		0
157.4	−1.58541	+	1.21921i	1.05085	+	1.05085i	1.02703	−	3.86590i		0		−2.94723	−	0.384812i	−3.45629	−	3.45629i	3.08510	+	7.38120i		−	6.79144i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
5.c	odd	4	2	inner
8.b	even	2	1	inner
40.f	even	2	1	inner
40.i	odd	4	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	200.3.i.c	✓	32
4.b	odd	2	1		800.3.m.c		32
5.b	even	2	1	inner	200.3.i.c	✓	32
5.c	odd	4	2	inner	200.3.i.c	✓	32
8.b	even	2	1	inner	200.3.i.c	✓	32
8.d	odd	2	1		800.3.m.c		32
20.d	odd	2	1		800.3.m.c		32
20.e	even	4	2		800.3.m.c		32
40.e	odd	2	1		800.3.m.c		32
40.f	even	2	1	inner	200.3.i.c	✓	32
40.i	odd	4	2	inner	200.3.i.c	✓	32
40.k	even	4	2		800.3.m.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
200.3.i.c	✓	32	1.a	even	1	1	trivial
200.3.i.c	✓	32	5.b	even	2	1	inner
200.3.i.c	✓	32	5.c	odd	4	2	inner
200.3.i.c	✓	32	8.b	even	2	1	inner
200.3.i.c	✓	32	40.f	even	2	1	inner
200.3.i.c	✓	32	40.i	odd	4	2	inner
800.3.m.c		32	4.b	odd	2	1
800.3.m.c		32	8.d	odd	2	1
800.3.m.c		32	20.d	odd	2	1
800.3.m.c		32	20.e	even	4	2
800.3.m.c		32	40.e	odd	2	1
800.3.m.c		32	40.k	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{16} + 1044T_{3}^{12} + 119190T_{3}^{8} + 3825396T_{3}^{4} + 15944049 \) acting on \(S_{3}^{\mathrm{new}}(200, [\chi])\).