Newform orbit 200.2.o.a

• Label: 200.2.o.a
• Level: $200$
• Weight: $2$
• Character orbit: 200.o
• Analytic conductor: $1.597$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.59700804043\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1	−1.41058	−	0.101294i	1.22940	+	0.893213i	1.97948	+	0.285768i	−0.369040	−	2.20540i	−1.64369	−	1.38448i		−	3.99458i	−2.76327	−	0.603610i	−0.213451	−	0.656936i	0.297166	+	3.14828i
29.2	−1.37194	+	0.343193i	−2.01785	−	1.46605i	1.76444	−	0.941679i	1.86593	−	1.23219i	3.27150	+	1.31882i			0.110917i	−2.09752	+	1.89747i	0.995348	+	3.06337i	−2.13706	+	2.33087i
29.3	−1.35766	−	0.395927i	1.59355	+	1.15778i	1.68648	+	1.07507i	2.17119	+	0.534744i	−1.70510	−	2.20281i			3.95226i	−1.86402	−	2.12730i	0.271894	+	0.836804i	−2.73601	−	1.58563i
29.4	−1.33109	−	0.477701i	−1.59355	−	1.15778i	1.54360	+	1.27173i	−2.17119	−	0.534744i	1.56809	+	2.30235i			3.95226i	−1.44717	−	2.43016i	0.271894	+	0.836804i	2.63460	+	1.74897i
29.5	−1.20072	−	0.747170i	−1.22940	−	0.893213i	0.883474	+	1.79429i	0.369040	+	2.20540i	0.808790	+	1.99107i		−	3.99458i	0.279830	−	2.81455i	−0.213451	−	0.656936i	1.20470	−	2.92382i
29.6	−1.20071	+	0.747190i	−0.235999	−	0.171463i	0.883414	−	1.79432i	−2.21228	+	0.325311i	0.411483	+	0.0295418i			0.234809i	0.279973	+	2.81454i	−0.900755	−	2.77224i	2.41324	−	2.04360i
29.7	−1.08090	+	0.911952i	2.58107	+	1.87526i	0.336688	−	1.97146i	0.602254	+	2.15344i	−4.50002	+	0.326846i		−	2.97769i	1.43395	+	2.43799i	2.21828	+	6.82716i	−2.61481	−	1.77842i
29.8	−1.01240	+	0.987445i	1.39188	+	1.01126i	0.0499066	−	1.99938i	0.122399	−	2.23272i	−2.40770	+	0.350605i			4.42380i	1.92375	+	2.07345i	−0.0123697	−	0.0380700i	2.08077	+	2.38126i
29.9	−0.908199	−	1.08405i	2.01785	+	1.46605i	−0.350349	+	1.96907i	−1.86593	+	1.23219i	−0.243326	−	3.51892i			0.110917i	2.45277	−	1.40851i	0.995348	+	3.06337i	3.03040	+	0.903693i
29.10	−0.717591	+	1.21863i	−2.54275	−	1.84742i	−0.970125	−	1.74896i	−1.08744	+	1.95384i	4.07598	−	1.77299i		−	1.17589i	2.82749	+	0.0728129i	2.12559	+	6.54190i	−1.60067	−	2.72724i
29.11	−0.556118	+	1.30028i	−0.0988780	−	0.0718391i	−1.38147	−	1.44622i	2.13827	−	0.654056i	0.148399	−	0.0886183i		−	4.12326i	2.64875	−	0.992028i	−0.922435	−	2.83896i	−0.338674	+	3.14409i
29.12	−0.532208	−	1.31025i	0.235999	+	0.171463i	−1.43351	+	1.39465i	2.21228	−	0.325311i	0.0990593	−	0.400472i			0.234809i	2.59027	+	1.13601i	−0.900755	−	2.77224i	−1.60363	−	2.72550i
29.13	−0.338435	−	1.37312i	−2.58107	−	1.87526i	−1.77092	+	0.929423i	−0.602254	−	2.15344i	−1.70143	+	4.17877i		−	2.97769i	1.87555	+	2.11714i	2.21828	+	6.82716i	−2.75311	+	1.55576i
29.14	−0.238643	−	1.39393i	−1.39188	−	1.01126i	−1.88610	+	0.665306i	−0.122399	+	2.23272i	−1.07746	+	2.18152i			4.42380i	1.37750	+	2.47032i	−0.0123697	−	0.0380700i	3.14147	−	0.362207i
29.15	−0.0299570	+	1.41390i	1.06117	+	0.770982i	−1.99821	−	0.0847122i	−1.15605	+	1.91404i	−1.12188	+	1.47728i			2.31589i	0.179635	−	2.82272i	−0.395392	−	1.21689i	−2.67162	−	1.69188i
29.16	0.135750	−	1.40768i	2.54275	+	1.84742i	−1.96314	−	0.382186i	1.08744	−	1.95384i	2.94576	−	3.32861i		−	1.17589i	−0.804493	+	2.71160i	2.12559	+	6.54190i	−2.60276	−	1.79600i
29.17	0.137018	+	1.40756i	−1.09282	−	0.793983i	−1.96245	+	0.385721i	−1.09814	−	1.94784i	0.967842	−	1.64700i		−	0.296885i	−0.811817	−	2.70942i	−0.363197	−	1.11780i	2.59124	−	1.81259i
29.18	0.314378	−	1.37883i	0.0988780	+	0.0718391i	−1.80233	−	0.866946i	−2.13827	+	0.654056i	0.130139	−	0.113751i		−	4.12326i	−1.76198	+	2.21256i	−0.922435	−	2.83896i	0.229604	+	3.15393i
29.19	0.658957	+	1.25131i	−2.03813	−	1.48079i	−1.13155	+	1.64912i	2.19360	+	0.433703i	0.509884	−	3.52610i			3.58786i	−2.80920	−	0.329223i	1.03418	+	3.18289i	0.902794	+	3.03067i
29.20	0.806832	−	1.16147i	−1.06117	−	0.770982i	−0.698045	−	1.87423i	1.15605	−	1.91404i	−1.75166	+	0.610464i			2.31589i	−2.74007	−	0.701425i	−0.395392	−	1.21689i	−1.29037	−	2.88703i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
25.e	even	10	1	inner
200.o	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	200.2.o.a	✓	112
4.b	odd	2	1		800.2.be.a		112
5.b	even	2	1		1000.2.o.a		112
5.c	odd	4	2		1000.2.t.b		224
8.b	even	2	1	inner	200.2.o.a	✓	112
8.d	odd	2	1		800.2.be.a		112
25.d	even	5	1		1000.2.o.a		112
25.e	even	10	1	inner	200.2.o.a	✓	112
25.f	odd	20	2		1000.2.t.b		224
40.f	even	2	1		1000.2.o.a		112
40.i	odd	4	2		1000.2.t.b		224
100.h	odd	10	1		800.2.be.a		112
200.o	even	10	1	inner	200.2.o.a	✓	112
200.s	odd	10	1		800.2.be.a		112
200.t	even	10	1		1000.2.o.a		112
200.x	odd	20	2		1000.2.t.b		224

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
200.2.o.a	✓	112	1.a	even	1	1	trivial
200.2.o.a	✓	112	8.b	even	2	1	inner
200.2.o.a	✓	112	25.e	even	10	1	inner
200.2.o.a	✓	112	200.o	even	10	1	inner
800.2.be.a		112	4.b	odd	2	1
800.2.be.a		112	8.d	odd	2	1
800.2.be.a		112	100.h	odd	10	1
800.2.be.a		112	200.s	odd	10	1
1000.2.o.a		112	5.b	even	2	1
1000.2.o.a		112	25.d	even	5	1
1000.2.o.a		112	40.f	even	2	1
1000.2.o.a		112	200.t	even	10	1
1000.2.t.b		224	5.c	odd	4	2
1000.2.t.b		224	25.f	odd	20	2
1000.2.t.b		224	40.i	odd	4	2
1000.2.t.b		224	200.x	odd	20	2

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(200, [\chi])\).