Newform orbit 195.2.m.a

• Label: 195.2.m.a
• Level: $195$
• Weight: $2$
• Character orbit: 195.m
• Analytic conductor: $1.557$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.55708283941\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{3} - 8 q^{6} - 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1	−1.89087	−	1.89087i	−1.66788	−	0.467098i			5.15076i	−1.82901	+	1.28635i	2.27052	+	4.03696i	0.451712	−	0.451712i	5.95768	−	5.95768i	2.56364	+	1.55813i	5.89075	+	1.02610i
53.2	−1.80512	−	1.80512i	0.605452	−	1.62278i			4.51694i	1.97850	−	1.04190i	−4.02224	+	1.83641i	1.80307	−	1.80307i	4.54338	−	4.54338i	−2.26686	−	1.96503i	−5.45218	−	1.69068i
53.3	−1.64851	−	1.64851i	1.69918	+	0.335852i			3.43518i	−0.0748465	+	2.23481i	−2.24746	−	3.35477i	−0.504953	+	0.504953i	2.36592	−	2.36592i	2.77441	+	1.14134i	3.80750	−	3.56073i
53.4	−1.45601	−	1.45601i	−1.32712	+	1.11299i			2.23994i	0.199686	−	2.22713i	3.55283	+	0.311782i	−2.01233	+	2.01233i	0.349362	−	0.349362i	0.522511	−	2.95415i	−3.53348	+	2.95199i
53.5	−1.31738	−	1.31738i	0.984142	−	1.42529i			1.47096i	−2.10533	−	0.753385i	−3.17414	+	0.581165i	−3.17590	+	3.17590i	−0.696941	+	0.696941i	−1.06293	−	2.80538i	1.78102	+	3.76600i
53.6	−1.06124	−	1.06124i	1.45525	+	0.939275i			0.252467i	1.58402	−	1.57825i	−0.547579	−	2.54117i	0.861313	−	0.861313i	−1.85455	+	1.85455i	1.23553	+	2.73377i	−3.35593	−	0.00612405i
53.7	−1.01857	−	1.01857i	−1.68481	+	0.401755i			0.0749575i	1.86592	+	1.23221i	2.12531	+	1.30688i	1.22650	−	1.22650i	−1.96078	+	1.96078i	2.67719	−	1.35376i	−0.645476	−	3.15565i
53.8	−0.862800	−	0.862800i	−1.14056	−	1.30350i		−	0.511152i	−0.830195	−	2.07624i	−0.140585	+	2.10874i	2.36951	−	2.36951i	−2.16662	+	2.16662i	−0.398237	+	2.97345i	−1.07509	+	2.50767i
53.9	−0.739875	−	0.739875i	0.0950948	+	1.72944i		−	0.905170i	−0.142547	+	2.23152i	1.20921	−	1.34993i	−2.72416	+	2.72416i	−2.14946	+	2.14946i	−2.98191	+	0.328921i	1.75651	−	1.54558i
53.10	−0.263900	−	0.263900i	1.72936	−	0.0965050i		−	1.86071i	−2.20816	+	0.352184i	−0.481847	−	0.430911i	1.75235	−	1.75235i	−1.01884	+	1.01884i	2.98137	−	0.333784i	0.675676	+	0.489793i
53.11	−0.252899	−	0.252899i	1.12127	−	1.32014i		−	1.87208i	1.67228	+	1.48441i	−0.617428	+	0.0502933i	0.510420	−	0.510420i	−0.979246	+	0.979246i	−0.485515	−	2.96045i	−0.0475119	−	0.798324i
53.12	−0.0628718	−	0.0628718i	−1.66043	−	0.492933i		−	1.99209i	−1.69987	+	1.45274i	0.0734024	+	0.135386i	−2.55754	+	2.55754i	−0.250990	+	0.250990i	2.51403	+	1.63696i	0.198210	+	0.0155376i
53.13	0.0628718	+	0.0628718i	−0.492933	−	1.66043i		−	1.99209i	1.69987	−	1.45274i	0.0734024	−	0.135386i	−2.55754	+	2.55754i	0.250990	−	0.250990i	−2.51403	+	1.63696i	0.198210	+	0.0155376i
53.14	0.252899	+	0.252899i	−1.32014	+	1.12127i		−	1.87208i	−1.67228	−	1.48441i	−0.617428	−	0.0502933i	0.510420	−	0.510420i	0.979246	−	0.979246i	0.485515	−	2.96045i	−0.0475119	−	0.798324i
53.15	0.263900	+	0.263900i	−0.0965050	+	1.72936i		−	1.86071i	2.20816	−	0.352184i	−0.481847	+	0.430911i	1.75235	−	1.75235i	1.01884	−	1.01884i	−2.98137	−	0.333784i	0.675676	+	0.489793i
53.16	0.739875	+	0.739875i	1.72944	+	0.0950948i		−	0.905170i	0.142547	−	2.23152i	1.20921	+	1.34993i	−2.72416	+	2.72416i	2.14946	−	2.14946i	2.98191	+	0.328921i	1.75651	−	1.54558i
53.17	0.862800	+	0.862800i	−1.30350	−	1.14056i		−	0.511152i	0.830195	+	2.07624i	−0.140585	−	2.10874i	2.36951	−	2.36951i	2.16662	−	2.16662i	0.398237	+	2.97345i	−1.07509	+	2.50767i
53.18	1.01857	+	1.01857i	0.401755	−	1.68481i			0.0749575i	−1.86592	−	1.23221i	2.12531	−	1.30688i	1.22650	−	1.22650i	1.96078	−	1.96078i	−2.67719	−	1.35376i	−0.645476	−	3.15565i
53.19	1.06124	+	1.06124i	0.939275	+	1.45525i			0.252467i	−1.58402	+	1.57825i	−0.547579	+	2.54117i	0.861313	−	0.861313i	1.85455	−	1.85455i	−1.23553	+	2.73377i	−3.35593	−	0.00612405i
53.20	1.31738	+	1.31738i	−1.42529	+	0.984142i			1.47096i	2.10533	+	0.753385i	−3.17414	−	0.581165i	−3.17590	+	3.17590i	0.696941	−	0.696941i	1.06293	−	2.80538i	1.78102	+	3.76600i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
15.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	195.2.m.a	✓	48
3.b	odd	2	1	inner	195.2.m.a	✓	48
5.b	even	2	1		975.2.m.d		48
5.c	odd	4	1	inner	195.2.m.a	✓	48
5.c	odd	4	1		975.2.m.d		48
15.d	odd	2	1		975.2.m.d		48
15.e	even	4	1	inner	195.2.m.a	✓	48
15.e	even	4	1		975.2.m.d		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
195.2.m.a	✓	48	1.a	even	1	1	trivial
195.2.m.a	✓	48	3.b	odd	2	1	inner
195.2.m.a	✓	48	5.c	odd	4	1	inner
195.2.m.a	✓	48	15.e	even	4	1	inner
975.2.m.d		48	5.b	even	2	1
975.2.m.d		48	5.c	odd	4	1
975.2.m.d		48	15.d	odd	2	1
975.2.m.d		48	15.e	even	4	1

Hecke kernels

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