Newform orbit 1183.2.c.j

• Label: 1183.2.c.j
• Level: $1183$
• Weight: $2$
• Character orbit: 1183.c
• Analytic conductor: $9.446$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.44630255912\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
337.1		−	2.62803i	−1.76762			−4.90656					2.94291i			4.64535i			1.00000i			7.63852i	0.124466			7.73406
337.2		−	2.58557i	2.93994			−4.68518					1.26031i		−	7.60143i		−	1.00000i			6.94272i	5.64327			3.25863
337.3		−	2.47725i	0.982981			−4.13677				−	1.35413i		−	2.43509i			1.00000i			5.29330i	−2.03375			−3.35452
337.4		−	2.23724i	3.02592			−3.00523					3.28547i		−	6.76971i			1.00000i			2.24893i	6.15622			7.35037
337.5		−	2.07140i	−3.01646			−2.29068				−	2.69245i			6.24828i		−	1.00000i			0.602118i	6.09903			−5.57713
337.6		−	2.06743i	2.11889			−2.27425				−	2.43928i		−	4.38065i			1.00000i			0.566992i	1.48970			−5.04303
337.7		−	1.35819i	3.39737			0.155322				−	0.772491i		−	4.61428i		−	1.00000i		−	2.92733i	8.54215			−1.04919
337.8		−	1.10989i	0.955760			0.768150				−	3.55862i		−	1.06079i		−	1.00000i		−	3.07233i	−2.08652			−3.94966
337.9		−	0.983820i	−1.57171			1.03210				−	0.398447i			1.54628i			1.00000i		−	2.98304i	−0.529731			−0.392000
337.10		−	0.961590i	−1.98737			1.07534					3.39320i			1.91103i		−	1.00000i		−	2.95722i	0.949635			3.26287
337.11		−	0.842530i	0.161973			1.29014					3.72786i		−	0.136467i			1.00000i		−	2.77204i	−2.97376			3.14083
337.12		−	0.149660i	2.76031			1.97760					4.13443i		−	0.413107i		−	1.00000i		−	0.595288i	4.61930			0.618759
337.13			0.149660i	2.76031			1.97760				−	4.13443i			0.413107i			1.00000i			0.595288i	4.61930			0.618759
337.14			0.842530i	0.161973			1.29014				−	3.72786i			0.136467i		−	1.00000i			2.77204i	−2.97376			3.14083
337.15			0.961590i	−1.98737			1.07534				−	3.39320i		−	1.91103i			1.00000i			2.95722i	0.949635			3.26287
337.16			0.983820i	−1.57171			1.03210					0.398447i		−	1.54628i		−	1.00000i			2.98304i	−0.529731			−0.392000
337.17			1.10989i	0.955760			0.768150					3.55862i			1.06079i			1.00000i			3.07233i	−2.08652			−3.94966
337.18			1.35819i	3.39737			0.155322					0.772491i			4.61428i			1.00000i			2.92733i	8.54215			−1.04919
337.19			2.06743i	2.11889			−2.27425					2.43928i			4.38065i		−	1.00000i		−	0.566992i	1.48970			−5.04303
337.20			2.07140i	−3.01646			−2.29068					2.69245i		−	6.24828i			1.00000i		−	0.602118i	6.09903			−5.57713

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1183.2.c.j		24
13.b	even	2	1	inner	1183.2.c.j		24
13.d	odd	4	1		1183.2.a.q	✓	12
13.d	odd	4	1		1183.2.a.r	yes	12
91.i	even	4	1		8281.2.a.cn		12
91.i	even	4	1		8281.2.a.cq		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1183.2.a.q	✓	12	13.d	odd	4	1
1183.2.a.r	yes	12	13.d	odd	4	1
1183.2.c.j		24	1.a	even	1	1	trivial
1183.2.c.j		24	13.b	even	2	1	inner
8281.2.a.cn		12	91.i	even	4	1
8281.2.a.cq		12	91.i	even	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 + 39*T2^22 + 661*T2^20 + 6390*T2^18 + 38898*T2^16 + 155486*T2^14 + 413755*T2^12 + 729610*T2^10 + 835014*T2^8 + 593266*T2^6 + 238217*T2^4 + 42595*T2^2 + 841