Newform orbit 165.3.g.c

• Label: 165.3.g.c
• Level: $165$
• Weight: $3$
• Character orbit: 165.g
• Analytic conductor: $4.496$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	165.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.49592436194\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 96 q^{4} - 18 q^{6} - 40 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1	−3.81101			2.57738	−	1.53530i	10.5238			−1.30531	−	4.82661i	−9.82240	+	5.85102i		−	9.94226i	−24.8621			4.28574	−	7.91407i	4.97455	+	18.3942i
89.2	−3.81101			2.57738	+	1.53530i	10.5238			−1.30531	+	4.82661i	−9.82240	−	5.85102i			9.94226i	−24.8621			4.28574	+	7.91407i	4.97455	−	18.3942i
89.3	−3.58971			−1.33898	−	2.68461i	8.88603			4.83928	+	1.25754i	4.80656	+	9.63697i			1.00797i	−17.5394			−5.41425	+	7.18929i	−17.3716	−	4.51419i
89.4	−3.58971			−1.33898	+	2.68461i	8.88603			4.83928	−	1.25754i	4.80656	−	9.63697i		−	1.00797i	−17.5394			−5.41425	−	7.18929i	−17.3716	+	4.51419i
89.5	−3.01474			−0.732962	−	2.90908i	5.08864			−4.85098	−	1.21160i	2.20969	+	8.77012i			9.10969i	−3.28198			−7.92553	+	4.26449i	14.6244	+	3.65266i
89.6	−3.01474			−0.732962	+	2.90908i	5.08864			−4.85098	+	1.21160i	2.20969	−	8.77012i		−	9.10969i	−3.28198			−7.92553	−	4.26449i	14.6244	−	3.65266i
89.7	−2.76973			−2.95390	−	0.523881i	3.67141			0.335292	−	4.98875i	8.18152	+	1.45101i		−	3.38200i	0.910114			8.45110	+	3.09499i	−0.928670	+	13.8175i
89.8	−2.76973			−2.95390	+	0.523881i	3.67141			0.335292	+	4.98875i	8.18152	−	1.45101i			3.38200i	0.910114			8.45110	−	3.09499i	−0.928670	−	13.8175i
89.9	−2.72754			1.64438	−	2.50919i	3.43950			−2.34112	+	4.41805i	−4.48511	+	6.84392i		−	5.12474i	1.52879			−3.59206	−	8.25210i	6.38551	−	12.0504i
89.10	−2.72754			1.64438	+	2.50919i	3.43950			−2.34112	−	4.41805i	−4.48511	−	6.84392i			5.12474i	1.52879			−3.59206	+	8.25210i	6.38551	+	12.0504i
89.11	−2.31979			2.83483	−	0.981702i	1.38141			3.52444	−	3.54660i	−6.57620	+	2.27734i			9.52264i	6.07457			7.07252	−	5.56592i	−8.17595	+	8.22735i
89.12	−2.31979			2.83483	+	0.981702i	1.38141			3.52444	+	3.54660i	−6.57620	−	2.27734i		−	9.52264i	6.07457			7.07252	+	5.56592i	−8.17595	−	8.22735i
89.13	−1.48137			−0.0395218	−	2.99974i	−1.80556			4.50776	−	2.16336i	0.0585462	+	4.44371i		−	5.90117i	8.60015			−8.99688	+	0.237110i	−6.67764	+	3.20472i
89.14	−1.48137			−0.0395218	+	2.99974i	−1.80556			4.50776	+	2.16336i	0.0585462	−	4.44371i			5.90117i	8.60015			−8.99688	−	0.237110i	−6.67764	−	3.20472i
89.15	−0.796683			−2.20488	−	2.03433i	−3.36530			1.97067	+	4.59527i	1.75659	+	1.62072i		−	0.558755i	5.86781			0.722982	+	8.97091i	−1.57000	−	3.66097i
89.16	−0.796683			−2.20488	+	2.03433i	−3.36530			1.97067	−	4.59527i	1.75659	−	1.62072i			0.558755i	5.86781			0.722982	−	8.97091i	−1.57000	+	3.66097i
89.17	−0.424380			1.48263	−	2.60803i	−3.81990			0.614153	+	4.96214i	−0.629198	+	1.10679i			10.6128i	3.31861			−4.60362	−	7.73348i	−0.260634	−	2.10583i
89.18	−0.424380			1.48263	+	2.60803i	−3.81990			0.614153	−	4.96214i	−0.629198	−	1.10679i		−	10.6128i	3.31861			−4.60362	+	7.73348i	−0.260634	+	2.10583i
89.19	0.424380			−1.48263	−	2.60803i	−3.81990			−0.614153	−	4.96214i	−0.629198	−	1.10679i			10.6128i	−3.31861			−4.60362	+	7.73348i	−0.260634	−	2.10583i
89.20	0.424380			−1.48263	+	2.60803i	−3.81990			−0.614153	+	4.96214i	−0.629198	+	1.10679i		−	10.6128i	−3.31861			−4.60362	−	7.73348i	−0.260634	+	2.10583i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	165.3.g.c	✓	36
3.b	odd	2	1	inner	165.3.g.c	✓	36
5.b	even	2	1	inner	165.3.g.c	✓	36
15.d	odd	2	1	inner	165.3.g.c	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
165.3.g.c	✓	36	1.a	even	1	1	trivial
165.3.g.c	✓	36	3.b	odd	2	1	inner
165.3.g.c	✓	36	5.b	even	2	1	inner
165.3.g.c	✓	36	15.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^18 - 60*T2^16 + 1496*T2^14 - 20088*T2^12 + 157118*T2^10 - 720464*T2^8 + 1840488*T2^6 - 2301464*T2^4 + 1086465*T2^2 - 131044