Newform orbit 483.2.m.a

• Label: 483.2.m.a
• Level: $483$
• Weight: $2$
• Character orbit: 483.m
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(60\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
137.1	−2.35341	+	1.35874i	1.22585	+	1.22364i	2.69235	−	4.66329i	−1.88300	−	3.26145i	−4.54753	−	1.21410i	−0.393331	−	2.61635i			9.19786i	0.00542953	+	3.00000i	8.86291	+	5.11701i
137.2	−2.35341	+	1.35874i	1.22585	+	1.22364i	2.69235	−	4.66329i	1.88300	+	3.26145i	−4.54753	−	1.21410i	0.393331	+	2.61635i			9.19786i	0.00542953	+	3.00000i	−8.86291	−	5.11701i
137.3	−2.20025	+	1.27031i	−1.66604	−	0.473602i	2.22739	−	3.85796i	−0.823724	−	1.42673i	4.26733	−	1.07436i	−2.24449	+	1.40082i			6.23669i	2.55140	+	1.57808i	3.62479	+	2.09277i
137.4	−2.20025	+	1.27031i	−1.66604	−	0.473602i	2.22739	−	3.85796i	0.823724	+	1.42673i	4.26733	−	1.07436i	2.24449	−	1.40082i			6.23669i	2.55140	+	1.57808i	−3.62479	−	2.09277i
137.5	−2.14419	+	1.23795i	−0.991594	+	1.42012i	2.06503	−	3.57673i	−0.969003	−	1.67836i	0.368129	−	4.27255i	0.562535	+	2.58526i			5.27380i	−1.03348	−	2.81637i	4.15545	+	2.39915i
137.6	−2.14419	+	1.23795i	−0.991594	+	1.42012i	2.06503	−	3.57673i	0.969003	+	1.67836i	0.368129	−	4.27255i	−0.562535	−	2.58526i			5.27380i	−1.03348	−	2.81637i	−4.15545	−	2.39915i
137.7	−2.05926	+	1.18892i	1.51759	−	0.834823i	1.82704	−	3.16453i	−0.178457	−	0.309097i	−2.13257	+	3.52340i	2.62376	+	0.340385i			3.93312i	1.60614	−	2.53383i	0.734981	+	0.424342i
137.8	−2.05926	+	1.18892i	1.51759	−	0.834823i	1.82704	−	3.16453i	0.178457	+	0.309097i	−2.13257	+	3.52340i	−2.62376	−	0.340385i			3.93312i	1.60614	−	2.53383i	−0.734981	−	0.424342i
137.9	−1.78161	+	1.02861i	0.0211372	−	1.73192i	1.11608	−	1.93311i	−1.27213	−	2.20340i	1.74382	+	3.10735i	−0.668238	−	2.55997i			0.477615i	−2.99911	−	0.0732160i	4.53288	+	2.61706i
137.10	−1.78161	+	1.02861i	0.0211372	−	1.73192i	1.11608	−	1.93311i	1.27213	+	2.20340i	1.74382	+	3.10735i	0.668238	+	2.55997i			0.477615i	−2.99911	−	0.0732160i	−4.53288	−	2.61706i
137.11	−1.55658	+	0.898694i	0.279659	+	1.70932i	0.615303	−	1.06574i	−0.620314	−	1.07442i	−1.97147	−	2.40938i	−2.49407	+	0.882968i		−	1.38290i	−2.84358	+	0.956058i	1.93114	+	1.11495i
137.12	−1.55658	+	0.898694i	0.279659	+	1.70932i	0.615303	−	1.06574i	0.620314	+	1.07442i	−1.97147	−	2.40938i	2.49407	−	0.882968i		−	1.38290i	−2.84358	+	0.956058i	−1.93114	−	1.11495i
137.13	−1.44748	+	0.835704i	1.59432	+	0.676852i	0.396802	−	0.687281i	−1.25144	−	2.16756i	−2.87340	+	0.352653i	2.40151	+	1.11029i		−	2.01638i	2.08374	+	2.15824i	3.62287	+	2.09167i
137.14	−1.44748	+	0.835704i	1.59432	+	0.676852i	0.396802	−	0.687281i	1.25144	+	2.16756i	−2.87340	+	0.352653i	−2.40151	−	1.11029i		−	2.01638i	2.08374	+	2.15824i	−3.62287	−	2.09167i
137.15	−1.28014	+	0.739089i	−1.73064	+	0.0699156i	0.0925045	−	0.160222i	−0.974027	−	1.68706i	2.16379	−	1.36860i	−2.08240	−	1.63205i		−	2.68288i	2.99022	−	0.241997i	2.49378	+	1.43978i
137.16	−1.28014	+	0.739089i	−1.73064	+	0.0699156i	0.0925045	−	0.160222i	0.974027	+	1.68706i	2.16379	−	1.36860i	2.08240	+	1.63205i		−	2.68288i	2.99022	−	0.241997i	−2.49378	−	1.43978i
137.17	−1.19221	+	0.688323i	1.08950	−	1.34647i	−0.0524225	+	0.0907985i	−2.03563	−	3.52582i	−0.372109	+	2.35521i	−1.00571	+	2.44715i		−	2.89763i	−0.625968	−	2.93397i	4.85381	+	2.80235i
137.18	−1.19221	+	0.688323i	1.08950	−	1.34647i	−0.0524225	+	0.0907985i	2.03563	+	3.52582i	−0.372109	+	2.35521i	1.00571	−	2.44715i		−	2.89763i	−0.625968	−	2.93397i	−4.85381	−	2.80235i
137.19	−0.935072	+	0.539864i	−0.991443	−	1.42023i	−0.417093	+	0.722427i	−0.281343	−	0.487300i	1.69380	+	0.792769i	−1.64560	+	2.07172i		−	3.06015i	−1.03408	+	2.81615i	0.526152	+	0.303774i
137.20	−0.935072	+	0.539864i	−0.991443	−	1.42023i	−0.417093	+	0.722427i	0.281343	+	0.487300i	1.69380	+	0.792769i	1.64560	−	2.07172i		−	3.06015i	−1.03408	+	2.81615i	−0.526152	−	0.303774i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
21.h	odd	6	1	inner
23.b	odd	2	1	inner
69.c	even	2	1	inner
161.f	odd	6	1	inner
483.m	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	483.2.m.a	✓	120
3.b	odd	2	1	inner	483.2.m.a	✓	120
7.c	even	3	1	inner	483.2.m.a	✓	120
21.h	odd	6	1	inner	483.2.m.a	✓	120
23.b	odd	2	1	inner	483.2.m.a	✓	120
69.c	even	2	1	inner	483.2.m.a	✓	120
161.f	odd	6	1	inner	483.2.m.a	✓	120
483.m	even	6	1	inner	483.2.m.a	✓	120

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
483.2.m.a	✓	120	1.a	even	1	1	trivial
483.2.m.a	✓	120	3.b	odd	2	1	inner
483.2.m.a	✓	120	7.c	even	3	1	inner
483.2.m.a	✓	120	21.h	odd	6	1	inner
483.2.m.a	✓	120	23.b	odd	2	1	inner
483.2.m.a	✓	120	69.c	even	2	1	inner
483.2.m.a	✓	120	161.f	odd	6	1	inner
483.2.m.a	✓	120	483.m	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(483, [\chi])\).