Newform orbit 1183.2.e.j

• Label: 1183.2.e.j
• Level: $1183$
• Weight: $2$
• Character orbit: 1183.e
• Analytic conductor: $9.446$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.44630255912\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
170.1	−1.29430	+	2.24179i	−0.259233	−	0.449005i	−2.35043	−	4.07106i	−0.806027	+	1.39608i	1.34210			2.13104	+	1.56802i	6.99143			1.36560	−	2.36528i	−2.08648	−	3.61389i
170.2	−1.15163	+	1.99469i	0.736680	+	1.27597i	−1.65252	−	2.86225i	−0.423646	+	0.733776i	−3.39354			−1.00088	−	2.44913i	3.00585			0.414604	−	0.718115i	−0.975769	−	1.69008i
170.3	−0.689527	+	1.19430i	−1.44060	−	2.49520i	0.0491037	+	0.0850501i	−0.402974	+	0.697972i	3.97334			−1.26180	−	2.32548i	−2.89354			−2.65067	+	4.59109i	−0.555723	−	0.962541i
170.4	−0.672613	+	1.16500i	−1.02505	−	1.77544i	0.0951832	+	0.164862i	−1.78389	+	3.08979i	2.75785			2.62255	−	0.349630i	−2.94654			−0.601462	+	1.04176i	−2.39973	−	4.15646i
170.5	−0.249993	+	0.433001i	−0.424801	−	0.735776i	0.875007	+	1.51556i	0.521238	−	0.902810i	0.424789			−2.40155	+	1.11021i	−1.87496			1.13909	−	1.97296i	0.260612	+	0.451393i
170.6	−0.0904119	+	0.156598i	0.913006	+	1.58137i	0.983651	+	1.70373i	−1.34332	+	2.32670i	−0.330186			−1.64912	+	2.06892i	−0.717383			−0.167162	+	0.289532i	−0.242904	−	0.420723i
170.7	0.0904119	−	0.156598i	0.913006	+	1.58137i	0.983651	+	1.70373i	1.34332	−	2.32670i	0.330186			1.64912	−	2.06892i	0.717383			−0.167162	+	0.289532i	−0.242904	−	0.420723i
170.8	0.249993	−	0.433001i	−0.424801	−	0.735776i	0.875007	+	1.51556i	−0.521238	+	0.902810i	−0.424789			2.40155	−	1.11021i	1.87496			1.13909	−	1.97296i	0.260612	+	0.451393i
170.9	0.672613	−	1.16500i	−1.02505	−	1.77544i	0.0951832	+	0.164862i	1.78389	−	3.08979i	−2.75785			−2.62255	+	0.349630i	2.94654			−0.601462	+	1.04176i	−2.39973	−	4.15646i
170.10	0.689527	−	1.19430i	−1.44060	−	2.49520i	0.0491037	+	0.0850501i	0.402974	−	0.697972i	−3.97334			1.26180	+	2.32548i	2.89354			−2.65067	+	4.59109i	−0.555723	−	0.962541i
170.11	1.15163	−	1.99469i	0.736680	+	1.27597i	−1.65252	−	2.86225i	0.423646	−	0.733776i	3.39354			1.00088	+	2.44913i	−3.00585			0.414604	−	0.718115i	−0.975769	−	1.69008i
170.12	1.29430	−	2.24179i	−0.259233	−	0.449005i	−2.35043	−	4.07106i	0.806027	−	1.39608i	−1.34210			−2.13104	−	1.56802i	−6.99143			1.36560	−	2.36528i	−2.08648	−	3.61389i
508.1	−1.29430	−	2.24179i	−0.259233	+	0.449005i	−2.35043	+	4.07106i	−0.806027	−	1.39608i	1.34210			2.13104	−	1.56802i	6.99143			1.36560	+	2.36528i	−2.08648	+	3.61389i
508.2	−1.15163	−	1.99469i	0.736680	−	1.27597i	−1.65252	+	2.86225i	−0.423646	−	0.733776i	−3.39354			−1.00088	+	2.44913i	3.00585			0.414604	+	0.718115i	−0.975769	+	1.69008i
508.3	−0.689527	−	1.19430i	−1.44060	+	2.49520i	0.0491037	−	0.0850501i	−0.402974	−	0.697972i	3.97334			−1.26180	+	2.32548i	−2.89354			−2.65067	−	4.59109i	−0.555723	+	0.962541i
508.4	−0.672613	−	1.16500i	−1.02505	+	1.77544i	0.0951832	−	0.164862i	−1.78389	−	3.08979i	2.75785			2.62255	+	0.349630i	−2.94654			−0.601462	−	1.04176i	−2.39973	+	4.15646i
508.5	−0.249993	−	0.433001i	−0.424801	+	0.735776i	0.875007	−	1.51556i	0.521238	+	0.902810i	0.424789			−2.40155	−	1.11021i	−1.87496			1.13909	+	1.97296i	0.260612	−	0.451393i
508.6	−0.0904119	−	0.156598i	0.913006	−	1.58137i	0.983651	−	1.70373i	−1.34332	−	2.32670i	−0.330186			−1.64912	−	2.06892i	−0.717383			−0.167162	−	0.289532i	−0.242904	+	0.420723i
508.7	0.0904119	+	0.156598i	0.913006	−	1.58137i	0.983651	−	1.70373i	1.34332	+	2.32670i	0.330186			1.64912	+	2.06892i	0.717383			−0.167162	−	0.289532i	−0.242904	+	0.420723i
508.8	0.249993	+	0.433001i	−0.424801	+	0.735776i	0.875007	−	1.51556i	−0.521238	−	0.902810i	−0.424789			2.40155	+	1.11021i	1.87496			1.13909	+	1.97296i	0.260612	−	0.451393i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
13.b	even	2	1	inner
91.r	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1183.2.e.j		24
7.c	even	3	1	inner	1183.2.e.j		24
7.c	even	3	1		8281.2.a.cp		12
7.d	odd	6	1		8281.2.a.co		12
13.b	even	2	1	inner	1183.2.e.j		24
13.f	odd	12	1		91.2.k.b	✓	12
13.f	odd	12	1		91.2.u.b	yes	12
39.k	even	12	1		819.2.bm.f		12
39.k	even	12	1		819.2.do.e		12
91.r	even	6	1	inner	1183.2.e.j		24
91.r	even	6	1		8281.2.a.cp		12
91.s	odd	6	1		8281.2.a.co		12
91.w	even	12	1		637.2.k.i		12
91.w	even	12	1		637.2.q.i		12
91.x	odd	12	1		91.2.u.b	yes	12
91.x	odd	12	1		637.2.q.g		12
91.ba	even	12	1		637.2.q.i		12
91.ba	even	12	1		637.2.u.g		12
91.bc	even	12	1		637.2.k.i		12
91.bc	even	12	1		637.2.u.g		12
91.bd	odd	12	1		91.2.k.b	✓	12
91.bd	odd	12	1		637.2.q.g		12
273.bv	even	12	1		819.2.do.e		12
273.bw	even	12	1		819.2.bm.f		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.2.k.b	✓	12	13.f	odd	12	1
91.2.k.b	✓	12	91.bd	odd	12	1
91.2.u.b	yes	12	13.f	odd	12	1
91.2.u.b	yes	12	91.x	odd	12	1
637.2.k.i		12	91.w	even	12	1
637.2.k.i		12	91.bc	even	12	1
637.2.q.g		12	91.x	odd	12	1
637.2.q.g		12	91.bd	odd	12	1
637.2.q.i		12	91.w	even	12	1
637.2.q.i		12	91.ba	even	12	1
637.2.u.g		12	91.ba	even	12	1
637.2.u.g		12	91.bc	even	12	1
819.2.bm.f		12	39.k	even	12	1
819.2.bm.f		12	273.bw	even	12	1
819.2.do.e		12	39.k	even	12	1
819.2.do.e		12	273.bv	even	12	1
1183.2.e.j		24	1.a	even	1	1	trivial
1183.2.e.j		24	7.c	even	3	1	inner
1183.2.e.j		24	13.b	even	2	1	inner
1183.2.e.j		24	91.r	even	6	1	inner
8281.2.a.co		12	7.d	odd	6	1
8281.2.a.co		12	91.s	odd	6	1
8281.2.a.cp		12	7.c	even	3	1
8281.2.a.cp		12	91.r	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1183, [\chi])\):

\( T_{2}^{24} + 16 T_{2}^{22} + 168 T_{2}^{20} + 1014 T_{2}^{18} + 4420 T_{2}^{16} + 11868 T_{2}^{14} + 23099 T_{2}^{12} + 27564 T_{2}^{10} + 22404 T_{2}^{8} + 5798 T_{2}^{6} + 1124 T_{2}^{4} + 36 T_{2}^{2} + 1 \)

\( T_{3}^{12} + 3 T_{3}^{11} + 14 T_{3}^{10} + 17 T_{3}^{9} + 69 T_{3}^{8} + 75 T_{3}^{7} + 233 T_{3}^{6} + 147 T_{3}^{5} + 355 T_{3}^{4} + 300 T_{3}^{3} + 333 T_{3}^{2} + 133 T_{3} + 49 \)