Newform orbit 585.2.bf.c

• Label: 585.2.bf.c
• Level: $585$
• Weight: $2$
• Character orbit: 585.bf
• Analytic conductor: $4.671$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.67124851824\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 20 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
199.1	−1.36408	+	2.36265i		0		−2.72141	−	4.71362i	−1.91068	+	1.16160i		0		1.86649	+	3.23285i	9.39252				0		−0.138139	−	6.09877i
199.2	−1.30511	+	2.26052i		0		−2.40664	−	4.16842i	2.09035	+	0.794006i		0		−0.372536	−	0.645251i	7.34329				0		−4.52301	+	3.68901i
199.3	−1.00561	+	1.74177i		0		−1.02251	−	1.77105i	−1.28334	−	1.83113i		0		−1.11175	−	1.92561i	0.0905636				0		4.47996	−	0.393873i
199.4	−0.946062	+	1.63863i		0		−0.790065	−	1.36843i	1.73576	+	1.40965i		0		−1.37597	−	2.38324i	−0.794445				0		−3.95204	+	1.51065i
199.5	−0.733363	+	1.27022i		0		−0.0756426	−	0.131017i	0.387771	+	2.20219i		0		2.16559	+	3.75091i	−2.71156				0		−3.08164	−	1.12245i
199.6	−0.611600	+	1.05932i		0		0.251890	+	0.436286i	−2.22227	−	0.247984i		0		−0.997778	−	1.72820i	−3.06263				0		1.62184	−	2.20244i
199.7	−0.296043	+	0.512762i		0		0.824717	+	1.42845i	0.903471	−	2.04542i		0		0.828705	+	1.43536i	−2.16078				0		0.781346	+	1.06880i
199.8	−0.173693	+	0.300844i		0		0.939662	+	1.62754i	−0.956446	+	2.02119i		0		−2.09191	−	3.62329i	−1.34762				0		−0.441936	−	0.638807i
199.9	0.173693	−	0.300844i		0		0.939662	+	1.62754i	0.956446	+	2.02119i		0		2.09191	+	3.62329i	1.34762				0		0.774192	+	0.0633244i
199.10	0.296043	−	0.512762i		0		0.824717	+	1.42845i	−0.903471	−	2.04542i		0		−0.828705	−	1.43536i	2.16078				0		−1.31628	−	0.142267i
199.11	0.611600	−	1.05932i		0		0.251890	+	0.436286i	2.22227	−	0.247984i		0		0.997778	+	1.72820i	3.06263				0		1.09645	−	2.50577i
199.12	0.733363	−	1.27022i		0		−0.0756426	−	0.131017i	−0.387771	+	2.20219i		0		−2.16559	−	3.75091i	2.71156				0		2.51289	+	2.10756i
199.13	0.946062	−	1.63863i		0		−0.790065	−	1.36843i	−1.73576	+	1.40965i		0		1.37597	+	2.38324i	0.794445				0		0.667754	+	4.17789i
199.14	1.00561	−	1.74177i		0		−1.02251	−	1.77105i	1.28334	−	1.83113i		0		1.11175	+	1.92561i	−0.0905636				0		−1.89887	−	4.07669i
199.15	1.30511	−	2.26052i		0		−2.40664	−	4.16842i	−2.09035	+	0.794006i		0		0.372536	+	0.645251i	−7.34329				0		−0.933271	+	5.76154i
199.16	1.36408	−	2.36265i		0		−2.72141	−	4.71362i	1.91068	+	1.16160i		0		−1.86649	−	3.23285i	−9.39252				0		5.35076	−	2.92975i
244.1	−1.36408	−	2.36265i		0		−2.72141	+	4.71362i	−1.91068	−	1.16160i		0		1.86649	−	3.23285i	9.39252				0		−0.138139	+	6.09877i
244.2	−1.30511	−	2.26052i		0		−2.40664	+	4.16842i	2.09035	−	0.794006i		0		−0.372536	+	0.645251i	7.34329				0		−4.52301	−	3.68901i
244.3	−1.00561	−	1.74177i		0		−1.02251	+	1.77105i	−1.28334	+	1.83113i		0		−1.11175	+	1.92561i	0.0905636				0		4.47996	+	0.393873i
244.4	−0.946062	−	1.63863i		0		−0.790065	+	1.36843i	1.73576	−	1.40965i		0		−1.37597	+	2.38324i	−0.794445				0		−3.95204	−	1.51065i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
13.e	even	6	1	inner
65.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	585.2.bf.c		32
3.b	odd	2	1		195.2.v.a	✓	32
5.b	even	2	1	inner	585.2.bf.c		32
13.e	even	6	1	inner	585.2.bf.c		32
15.d	odd	2	1		195.2.v.a	✓	32
15.e	even	4	1		975.2.bc.m		16
15.e	even	4	1		975.2.bc.n		16
39.h	odd	6	1		195.2.v.a	✓	32
65.l	even	6	1	inner	585.2.bf.c		32
195.y	odd	6	1		195.2.v.a	✓	32
195.bf	even	12	1		975.2.bc.m		16
195.bf	even	12	1		975.2.bc.n		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
195.2.v.a	✓	32	3.b	odd	2	1
195.2.v.a	✓	32	15.d	odd	2	1
195.2.v.a	✓	32	39.h	odd	6	1
195.2.v.a	✓	32	195.y	odd	6	1
585.2.bf.c		32	1.a	even	1	1	trivial
585.2.bf.c		32	5.b	even	2	1	inner
585.2.bf.c		32	13.e	even	6	1	inner
585.2.bf.c		32	65.l	even	6	1	inner
975.2.bc.m		16	15.e	even	4	1
975.2.bc.m		16	195.bf	even	12	1
975.2.bc.n		16	15.e	even	4	1
975.2.bc.n		16	195.bf	even	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 + 26*T2^30 + 407*T2^28 + 4154*T2^26 + 31361*T2^24 + 176092*T2^22 + 765152*T2^20 + 2542044*T2^18 + 6551308*T2^16 + 12675732*T2^14 + 18472664*T2^12 + 18771504*T2^10 + 13215808*T2^8 + 4856576*T2^6 + 1243664*T2^4 + 130800*T2^2 + 10000