Newform orbit 185.3.i.a

• Label: 185.3.i.a
• Level: $185$
• Weight: $3$
• Character orbit: 185.i
• Analytic conductor: $5.041$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	185.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.04088489067\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 4 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
38.1	−2.76393	+	2.76393i	−0.172777	−	0.172777i		−	11.2786i	4.95722	+	0.652635i	0.955086			−7.75504	+	7.75504i	20.1174	+	20.1174i		−	8.94030i	−15.5052	+	11.8976i
38.2	−2.57505	+	2.57505i	−1.21188	−	1.21188i		−	9.26173i	−4.74988	+	1.56163i	6.24128			3.35221	−	3.35221i	13.5492	+	13.5492i		−	6.06271i	8.20988	−	16.2524i
38.3	−2.45131	+	2.45131i	3.91833	+	3.91833i		−	8.01781i	4.61684	−	1.91958i	−19.2101			7.28156	−	7.28156i	9.84889	+	9.84889i			21.7066i	−6.61181	+	16.0228i
38.4	−2.31452	+	2.31452i	1.44768	+	1.44768i		−	6.71402i	−1.64719	−	4.72089i	−6.70139			−2.74688	+	2.74688i	6.28167	+	6.28167i		−	4.80842i	14.7391	+	7.11413i
38.5	−2.21996	+	2.21996i	−3.12499	−	3.12499i		−	5.85648i	0.517339	−	4.97316i	13.8747			2.12398	−	2.12398i	4.12131	+	4.12131i			10.5311i	9.89177	+	12.1887i
38.6	−2.15910	+	2.15910i	0.350378	+	0.350378i		−	5.32340i	2.00797	+	4.57909i	−1.51300			9.05676	−	9.05676i	2.85734	+	2.85734i		−	8.75447i	−14.2221	−	5.55131i
38.7	−1.94693	+	1.94693i	−3.37796	−	3.37796i		−	3.58104i	−2.50744	+	4.32582i	13.1533			−7.41851	+	7.41851i	−0.815680	−	0.815680i			13.8213i	−3.54026	−	13.3039i
38.8	−1.78549	+	1.78549i	2.24889	+	2.24889i		−	2.37598i	0.683599	+	4.95305i	−8.03076			−4.39956	+	4.39956i	−2.89968	−	2.89968i			1.11500i	−10.0642	−	7.62308i
38.9	−1.69755	+	1.69755i	2.44937	+	2.44937i		−	1.76335i	−4.35200	−	2.46173i	−8.31585			0.691017	−	0.691017i	−3.79683	−	3.79683i			2.99881i	11.5666	−	3.20884i
38.10	−1.41633	+	1.41633i	−0.698806	−	0.698806i		−	0.0120067i	4.28414	−	2.57801i	1.97949			1.63072	−	1.63072i	−5.64833	−	5.64833i		−	8.02334i	−2.41646	+	9.71910i
38.11	−1.39605	+	1.39605i	−1.91632	−	1.91632i			0.102063i	4.87251	+	1.12191i	5.35057			−2.42844	+	2.42844i	−5.72670	−	5.72670i		−	1.65546i	−8.36853	+	5.23604i
38.12	−1.09770	+	1.09770i	−0.567524	−	0.567524i			1.59009i	−4.95343	+	0.680845i	1.24595			−0.715080	+	0.715080i	−6.13627	−	6.13627i		−	8.35583i	4.69003	−	6.18476i
38.13	−0.953639	+	0.953639i	3.38619	+	3.38619i			2.18114i	3.98242	−	3.02330i	−6.45840			−8.81295	+	8.81295i	−5.89458	−	5.89458i			13.9325i	−0.914646	+	6.68093i
38.14	−0.703482	+	0.703482i	−3.36273	−	3.36273i			3.01023i	0.818175	+	4.93260i	4.73125			7.76444	−	7.76444i	−4.93157	−	4.93157i			13.6160i	−4.04557	−	2.89443i
38.15	−0.630278	+	0.630278i	1.16852	+	1.16852i			3.20550i	0.304603	−	4.99071i	−1.47299			8.64288	−	8.64288i	−4.54147	−	4.54147i		−	6.26910i	2.95355	+	3.33752i
38.16	−0.589419	+	0.589419i	3.93943	+	3.93943i			3.30517i	−4.04076	+	2.94488i	−4.64395			4.91172	−	4.91172i	−4.30580	−	4.30580i			22.0382i	0.645933	−	4.11746i
38.17	−0.317895	+	0.317895i	−3.52336	−	3.52336i			3.79789i	−3.50116	−	3.56957i	2.24011			−0.360962	+	0.360962i	−2.47891	−	2.47891i			15.8281i	2.24775	+	0.0217463i
38.18	−0.140304	+	0.140304i	−1.00120	−	1.00120i			3.96063i	−0.0593484	−	4.99965i	0.280943			−7.21630	+	7.21630i	−1.11690	−	1.11690i		−	6.99520i	0.709795	+	0.693142i
38.19	−0.0519304	+	0.0519304i	−0.0572691	−	0.0572691i			3.99461i	−2.47701	+	4.34332i	0.00594801			−2.29628	+	2.29628i	−0.415163	−	0.415163i		−	8.99344i	−0.0969182	−	0.354182i
38.20	0.132506	−	0.132506i	2.11251	+	2.11251i			3.96488i	4.36673	+	2.43550i	0.559842			2.41329	−	2.41329i	1.05540	+	1.05540i		−	0.0745903i	0.901338	−	0.255900i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	185.3.i.a	✓	72
5.c	odd	4	1	inner	185.3.i.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
185.3.i.a	✓	72	1.a	even	1	1	trivial
185.3.i.a	✓	72	5.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(185, [\chi])\).