Newform orbit 165.3.i.a

• Label: 165.3.i.a
• Level: $165$
• Weight: $3$
• Character orbit: 165.i
• Analytic conductor: $4.496$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	165.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.49592436194\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 24 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
67.1	−2.68034	−	2.68034i	1.22474	−	1.22474i			10.3684i	2.02776	−	4.57036i	−6.56546			6.22535	+	6.22535i	17.0696	−	17.0696i		−	3.00000i	−17.6852	+	6.81502i
67.2	−2.39583	−	2.39583i	−1.22474	+	1.22474i			7.48000i	0.478389	−	4.97706i	5.86856			−5.78823	−	5.78823i	8.33749	−	8.33749i		−	3.00000i	−13.0703	+	10.7781i
67.3	−2.15217	−	2.15217i	−1.22474	+	1.22474i			5.26367i	−1.03004	+	4.89275i	5.27172			−3.11675	−	3.11675i	2.71963	−	2.71963i		−	3.00000i	12.7468	−	8.31322i
67.4	−1.94815	−	1.94815i	−1.22474	+	1.22474i			3.59060i	−4.37927	−	2.41287i	4.77198			7.18811	+	7.18811i	−0.797579	+	0.797579i		−	3.00000i	3.83084	+	13.2321i
67.5	−1.73244	−	1.73244i	1.22474	−	1.22474i			2.00271i	−3.81685	−	3.22980i	−4.24360			−0.752612	−	0.752612i	−3.46019	+	3.46019i		−	3.00000i	1.01703	+	12.2079i
67.6	−0.955072	−	0.955072i	−1.22474	+	1.22474i		−	2.17567i	1.48130	+	4.77554i	2.33944			−1.91827	−	1.91827i	−5.89822	+	5.89822i		−	3.00000i	3.14623	−	5.97573i
67.7	−0.846751	−	0.846751i	−1.22474	+	1.22474i		−	2.56603i	3.20095	−	3.84108i	2.07411			−0.424617	−	0.424617i	−5.55979	+	5.55979i		−	3.00000i	−5.96285	+	0.542028i
67.8	−0.583847	−	0.583847i	1.22474	−	1.22474i		−	3.31824i	2.30754	−	4.43568i	−1.43013			−1.60383	−	1.60383i	−4.27274	+	4.27274i		−	3.00000i	−3.93701	+	1.24251i
67.9	−0.201521	−	0.201521i	1.22474	−	1.22474i		−	3.91878i	4.39623	+	2.38183i	−0.493623			7.35264	+	7.35264i	−1.59580	+	1.59580i		−	3.00000i	−0.405944	−	1.36592i
67.10	0.0108790	+	0.0108790i	1.22474	−	1.22474i		−	3.99976i	−2.44059	+	4.36389i	0.0266481			−9.31989	−	9.31989i	0.0870297	−	0.0870297i		−	3.00000i	−0.0740261	+	0.0209236i
67.11	0.417300	+	0.417300i	−1.22474	+	1.22474i		−	3.65172i	4.89447	+	1.02185i	−1.02217			−3.35695	−	3.35695i	3.19306	−	3.19306i		−	3.00000i	1.61604	+	2.46888i
67.12	1.12206	+	1.12206i	1.22474	−	1.22474i		−	1.48196i	−3.94513	−	3.07179i	2.74848			−0.560388	−	0.560388i	6.15109	−	6.15109i		−	3.00000i	−0.979943	−	7.87342i
67.13	1.24046	+	1.24046i	−1.22474	+	1.22474i		−	0.922536i	−2.40150	−	4.38552i	−3.03848			−7.57783	−	7.57783i	6.10619	−	6.10619i		−	3.00000i	2.46109	−	8.41900i
67.14	1.38623	+	1.38623i	−1.22474	+	1.22474i		−	0.156737i	2.64795	−	4.24127i	−3.39555			8.01657	+	8.01657i	5.76219	−	5.76219i		−	3.00000i	9.55003	−	2.20871i
67.15	1.55476	+	1.55476i	1.22474	−	1.22474i			0.834532i	4.73924	−	1.59362i	3.80836			−2.70293	−	2.70293i	4.92153	−	4.92153i		−	3.00000i	9.84604	+	4.89068i
67.16	1.68457	+	1.68457i	1.22474	−	1.22474i			1.67555i	−1.10192	+	4.87707i	4.12634			5.49033	+	5.49033i	3.91570	−	3.91570i		−	3.00000i	−10.0720	+	6.35950i
67.17	2.28477	+	2.28477i	−1.22474	+	1.22474i			6.44039i	4.09852	+	2.86394i	−5.59653			0.283118	+	0.283118i	−5.57574	+	5.57574i		−	3.00000i	2.82073	+	15.9076i
67.18	2.51973	+	2.51973i	−1.22474	+	1.22474i			8.69804i	−4.99077	+	0.303732i	−6.17204			1.79588	+	1.79588i	−11.8378	+	11.8378i		−	3.00000i	−13.3407	−	11.8100i
67.19	2.59307	+	2.59307i	1.22474	−	1.22474i			9.44805i	−0.878029	−	4.92230i	6.35170			7.87228	+	7.87228i	−14.1272	+	14.1272i		−	3.00000i	10.4871	−	15.0407i
67.20	2.68230	+	2.68230i	1.22474	−	1.22474i			10.3895i	2.71175	+	4.20076i	6.57027			−7.10197	−	7.10197i	−17.1385	+	17.1385i		−	3.00000i	−3.99399	+	18.5414i

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	165.3.i.a	✓	40
3.b	odd	2	1		495.3.j.b		40
5.c	odd	4	1	inner	165.3.i.a	✓	40
15.e	even	4	1		495.3.j.b		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
165.3.i.a	✓	40	1.a	even	1	1	trivial
165.3.i.a	✓	40	5.c	odd	4	1	inner
495.3.j.b		40	3.b	odd	2	1
495.3.j.b		40	15.e	even	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(165, [\chi])\).