Newform orbit 183.2.g.c

• Label: 183.2.g.c
• Level: $183$
• Weight: $2$
• Character orbit: 183.g
• Analytic conductor: $1.461$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.46126235699\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.79987	+	1.79987i	1.70524	−	0.303587i		−	4.47903i	0.391521			−2.52278	+	3.61561i	−0.663363	−	0.663363i	4.46193	+	4.46193i	2.81567	−	1.03538i	−0.704685	+	0.704685i
11.2	−1.53906	+	1.53906i	−1.73072	+	0.0678001i		−	2.73741i	3.09885			2.55934	−	2.76803i	1.25340	+	1.25340i	1.13492	+	1.13492i	2.99081	−	0.234686i	−4.76932	+	4.76932i
11.3	−1.24687	+	1.24687i	−0.576151	−	1.63342i		−	1.10936i	1.59774			2.75504	+	1.31827i	−2.44546	−	2.44546i	−1.11052	−	1.11052i	−2.33610	+	1.88219i	−1.99217	+	1.99217i
11.4	−1.06450	+	1.06450i	0.815973	−	1.52781i		−	0.266334i	−4.01835			0.757748	+	2.49496i	−0.934712	−	0.934712i	−1.84549	−	1.84549i	−1.66838	−	2.49329i	4.27754	−	4.27754i
11.5	−0.977222	+	0.977222i	1.38794	+	1.03616i			0.0900743i	−0.568356			−2.36888	+	0.343769i	1.94283	+	1.94283i	−2.04247	−	2.04247i	0.852753	+	2.87625i	0.555410	−	0.555410i
11.6	−0.379018	+	0.379018i	−0.171716	+	1.72352i			1.71269i	3.88753			−0.588160	−	0.718327i	−0.228336	−	0.228336i	−1.40718	−	1.40718i	−2.94103	−	0.591911i	−1.47344	+	1.47344i
11.7	−0.324526	+	0.324526i	−1.06918	−	1.36267i			1.78937i	−0.328679			0.789197	+	0.0952453i	2.07564	+	2.07564i	−1.22975	−	1.22975i	−0.713723	+	2.91386i	0.106665	−	0.106665i
11.8	0.324526	−	0.324526i	1.06918	−	1.36267i			1.78937i	0.328679			−0.0952453	−	0.789197i	2.07564	+	2.07564i	1.22975	+	1.22975i	−0.713723	−	2.91386i	0.106665	−	0.106665i
11.9	0.379018	−	0.379018i	0.171716	+	1.72352i			1.71269i	−3.88753			0.718327	+	0.588160i	−0.228336	−	0.228336i	1.40718	+	1.40718i	−2.94103	+	0.591911i	−1.47344	+	1.47344i
11.10	0.977222	−	0.977222i	−1.38794	+	1.03616i			0.0900743i	0.568356			−0.343769	+	2.36888i	1.94283	+	1.94283i	2.04247	+	2.04247i	0.852753	−	2.87625i	0.555410	−	0.555410i
11.11	1.06450	−	1.06450i	−0.815973	−	1.52781i		−	0.266334i	4.01835			−2.49496	−	0.757748i	−0.934712	−	0.934712i	1.84549	+	1.84549i	−1.66838	+	2.49329i	4.27754	−	4.27754i
11.12	1.24687	−	1.24687i	0.576151	−	1.63342i		−	1.10936i	−1.59774			−1.31827	−	2.75504i	−2.44546	−	2.44546i	1.11052	+	1.11052i	−2.33610	−	1.88219i	−1.99217	+	1.99217i
11.13	1.53906	−	1.53906i	1.73072	+	0.0678001i		−	2.73741i	−3.09885			2.76803	−	2.55934i	1.25340	+	1.25340i	−1.13492	−	1.13492i	2.99081	+	0.234686i	−4.76932	+	4.76932i
11.14	1.79987	−	1.79987i	−1.70524	−	0.303587i		−	4.47903i	−0.391521			−3.61561	+	2.52278i	−0.663363	−	0.663363i	−4.46193	−	4.46193i	2.81567	+	1.03538i	−0.704685	+	0.704685i
50.1	−1.79987	−	1.79987i	1.70524	+	0.303587i			4.47903i	0.391521			−2.52278	−	3.61561i	−0.663363	+	0.663363i	4.46193	−	4.46193i	2.81567	+	1.03538i	−0.704685	−	0.704685i
50.2	−1.53906	−	1.53906i	−1.73072	−	0.0678001i			2.73741i	3.09885			2.55934	+	2.76803i	1.25340	−	1.25340i	1.13492	−	1.13492i	2.99081	+	0.234686i	−4.76932	−	4.76932i
50.3	−1.24687	−	1.24687i	−0.576151	+	1.63342i			1.10936i	1.59774			2.75504	−	1.31827i	−2.44546	+	2.44546i	−1.11052	+	1.11052i	−2.33610	−	1.88219i	−1.99217	−	1.99217i
50.4	−1.06450	−	1.06450i	0.815973	+	1.52781i			0.266334i	−4.01835			0.757748	−	2.49496i	−0.934712	+	0.934712i	−1.84549	+	1.84549i	−1.66838	+	2.49329i	4.27754	+	4.27754i
50.5	−0.977222	−	0.977222i	1.38794	−	1.03616i		−	0.0900743i	−0.568356			−2.36888	−	0.343769i	1.94283	−	1.94283i	−2.04247	+	2.04247i	0.852753	−	2.87625i	0.555410	+	0.555410i
50.6	−0.379018	−	0.379018i	−0.171716	−	1.72352i		−	1.71269i	3.88753			−0.588160	+	0.718327i	−0.228336	+	0.228336i	−1.40718	+	1.40718i	−2.94103	+	0.591911i	−1.47344	−	1.47344i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
61.d	odd	4	1	inner
183.g	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	183.2.g.c	✓	28
3.b	odd	2	1	inner	183.2.g.c	✓	28
61.d	odd	4	1	inner	183.2.g.c	✓	28
183.g	even	4	1	inner	183.2.g.c	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
183.2.g.c	✓	28	1.a	even	1	1	trivial
183.2.g.c	✓	28	3.b	odd	2	1	inner
183.2.g.c	✓	28	61.d	odd	4	1	inner
183.2.g.c	✓	28	183.g	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} + 83T_{2}^{24} + 2245T_{2}^{20} + 24527T_{2}^{16} + 112415T_{2}^{12} + 184621T_{2}^{8} + 22059T_{2}^{4} + 625 \) acting on \(S_{2}^{\mathrm{new}}(183, [\chi])\).