Newform orbit 195.2.v.a

• Label: 195.2.v.a
• Level: $195$
• Weight: $2$
• Character orbit: 195.v
• Analytic conductor: $1.557$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.55708283941\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−1.36408	+	2.36265i	0.866025	+	0.500000i	−2.72141	−	4.71362i	−1.91068	−	1.16160i	−2.36265	+	1.36408i	−1.86649	−	3.23285i	9.39252			0.500000	+	0.866025i	5.35076	−	2.92975i
4.2	−1.30511	+	2.26052i	−0.866025	−	0.500000i	−2.40664	−	4.16842i	2.09035	−	0.794006i	2.26052	−	1.30511i	0.372536	+	0.645251i	7.34329			0.500000	+	0.866025i	−0.933271	+	5.76154i
4.3	−1.00561	+	1.74177i	−0.866025	−	0.500000i	−1.02251	−	1.77105i	−1.28334	+	1.83113i	1.74177	−	1.00561i	1.11175	+	1.92561i	0.0905636			0.500000	+	0.866025i	−1.89887	−	4.07669i
4.4	−0.946062	+	1.63863i	0.866025	+	0.500000i	−0.790065	−	1.36843i	1.73576	−	1.40965i	−1.63863	+	0.946062i	1.37597	+	2.38324i	−0.794445			0.500000	+	0.866025i	0.667754	+	4.17789i
4.5	−0.733363	+	1.27022i	−0.866025	−	0.500000i	−0.0756426	−	0.131017i	0.387771	−	2.20219i	1.27022	−	0.733363i	−2.16559	−	3.75091i	−2.71156			0.500000	+	0.866025i	2.51289	+	2.10756i
4.6	−0.611600	+	1.05932i	0.866025	+	0.500000i	0.251890	+	0.436286i	−2.22227	+	0.247984i	−1.05932	+	0.611600i	0.997778	+	1.72820i	−3.06263			0.500000	+	0.866025i	1.09645	−	2.50577i
4.7	−0.296043	+	0.512762i	0.866025	+	0.500000i	0.824717	+	1.42845i	0.903471	+	2.04542i	−0.512762	+	0.296043i	−0.828705	−	1.43536i	−2.16078			0.500000	+	0.866025i	−1.31628	−	0.142267i
4.8	−0.173693	+	0.300844i	−0.866025	−	0.500000i	0.939662	+	1.62754i	−0.956446	−	2.02119i	0.300844	−	0.173693i	2.09191	+	3.62329i	−1.34762			0.500000	+	0.866025i	0.774192	+	0.0633244i
4.9	0.173693	−	0.300844i	0.866025	+	0.500000i	0.939662	+	1.62754i	0.956446	−	2.02119i	0.300844	−	0.173693i	−2.09191	−	3.62329i	1.34762			0.500000	+	0.866025i	−0.441936	−	0.638807i
4.10	0.296043	−	0.512762i	−0.866025	−	0.500000i	0.824717	+	1.42845i	−0.903471	+	2.04542i	−0.512762	+	0.296043i	0.828705	+	1.43536i	2.16078			0.500000	+	0.866025i	0.781346	+	1.06880i
4.11	0.611600	−	1.05932i	−0.866025	−	0.500000i	0.251890	+	0.436286i	2.22227	+	0.247984i	−1.05932	+	0.611600i	−0.997778	−	1.72820i	3.06263			0.500000	+	0.866025i	1.62184	−	2.20244i
4.12	0.733363	−	1.27022i	0.866025	+	0.500000i	−0.0756426	−	0.131017i	−0.387771	−	2.20219i	1.27022	−	0.733363i	2.16559	+	3.75091i	2.71156			0.500000	+	0.866025i	−3.08164	−	1.12245i
4.13	0.946062	−	1.63863i	−0.866025	−	0.500000i	−0.790065	−	1.36843i	−1.73576	−	1.40965i	−1.63863	+	0.946062i	−1.37597	−	2.38324i	0.794445			0.500000	+	0.866025i	−3.95204	+	1.51065i
4.14	1.00561	−	1.74177i	0.866025	+	0.500000i	−1.02251	−	1.77105i	1.28334	+	1.83113i	1.74177	−	1.00561i	−1.11175	−	1.92561i	−0.0905636			0.500000	+	0.866025i	4.47996	−	0.393873i
4.15	1.30511	−	2.26052i	0.866025	+	0.500000i	−2.40664	−	4.16842i	−2.09035	−	0.794006i	2.26052	−	1.30511i	−0.372536	−	0.645251i	−7.34329			0.500000	+	0.866025i	−4.52301	+	3.68901i
4.16	1.36408	−	2.36265i	−0.866025	−	0.500000i	−2.72141	−	4.71362i	1.91068	−	1.16160i	−2.36265	+	1.36408i	1.86649	+	3.23285i	−9.39252			0.500000	+	0.866025i	−0.138139	−	6.09877i
49.1	−1.36408	−	2.36265i	0.866025	−	0.500000i	−2.72141	+	4.71362i	−1.91068	+	1.16160i	−2.36265	−	1.36408i	−1.86649	+	3.23285i	9.39252			0.500000	−	0.866025i	5.35076	+	2.92975i
49.2	−1.30511	−	2.26052i	−0.866025	+	0.500000i	−2.40664	+	4.16842i	2.09035	+	0.794006i	2.26052	+	1.30511i	0.372536	−	0.645251i	7.34329			0.500000	−	0.866025i	−0.933271	−	5.76154i
49.3	−1.00561	−	1.74177i	−0.866025	+	0.500000i	−1.02251	+	1.77105i	−1.28334	−	1.83113i	1.74177	+	1.00561i	1.11175	−	1.92561i	0.0905636			0.500000	−	0.866025i	−1.89887	+	4.07669i
49.4	−0.946062	−	1.63863i	0.866025	−	0.500000i	−0.790065	+	1.36843i	1.73576	+	1.40965i	−1.63863	−	0.946062i	1.37597	−	2.38324i	−0.794445			0.500000	−	0.866025i	0.667754	−	4.17789i

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	195.2.v.a	✓	32
3.b	odd	2	1		585.2.bf.c		32
5.b	even	2	1	inner	195.2.v.a	✓	32
5.c	odd	4	1		975.2.bc.m		16
5.c	odd	4	1		975.2.bc.n		16
13.e	even	6	1	inner	195.2.v.a	✓	32
15.d	odd	2	1		585.2.bf.c		32
39.h	odd	6	1		585.2.bf.c		32
65.l	even	6	1	inner	195.2.v.a	✓	32
65.r	odd	12	1		975.2.bc.m		16
65.r	odd	12	1		975.2.bc.n		16
195.y	odd	6	1		585.2.bf.c		32

    

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

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(195, [\chi])\).