Newform orbit 123.4.n.a

• Label: 123.4.n.a
• Level: $123$
• Weight: $4$
• Character orbit: 123.n
• Analytic conductor: $7.257$
• Analytic rank: $0$
• Dimension: $176$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	123.n (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.25723493071\)
Analytic rank:	\(0\)
Dimension:	\(176\)
Relative dimension:	\(22\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 176 q + 192 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−5.01276	+	1.62874i	−2.12132	+	2.12132i	16.0028	−	11.6267i	3.18507	+	4.38387i	7.17858	−	14.0888i	−0.114430	−	0.224582i	−36.4969	+	50.2337i		−	9.00000i	−23.1062	−	16.7876i
43.2	−4.97387	+	1.61611i	2.12132	−	2.12132i	15.6554	−	11.3743i	−8.95578	−	12.3266i	−7.12288	+	13.9794i	−14.5452	−	28.5466i	−34.8937	+	48.0270i		−	9.00000i	64.4659	+	46.8372i
43.3	−4.60341	+	1.49574i	2.12132	−	2.12132i	12.4821	−	9.06874i	10.8568	+	14.9431i	−6.59237	+	12.9383i	−1.32682	−	2.60403i	−21.1350	+	29.0899i		−	9.00000i	−72.3294	−	52.5504i
43.4	−3.78698	+	1.23047i	−2.12132	+	2.12132i	6.35505	−	4.61722i	−11.9602	−	16.4618i	5.42319	−	10.6436i	5.49955	+	10.7935i	0.338722	−	0.466211i		−	9.00000i	65.5486	+	47.6239i
43.5	−3.49722	+	1.13632i	2.12132	−	2.12132i	4.46719	−	3.24560i	−2.71030	−	3.73041i	−5.00823	+	9.82921i	6.55454	+	12.8640i	5.35649	−	7.37258i		−	9.00000i	13.7174	+	9.96630i
43.6	−3.18740	+	1.03565i	−2.12132	+	2.12132i	2.61479	−	1.89976i	10.5467	+	14.5162i	4.56455	−	8.95843i	8.43535	+	16.5553i	9.39246	−	12.9276i		−	9.00000i	−48.6501	−	35.3463i
43.7	−2.77214	+	0.900724i	−2.12132	+	2.12132i	0.401334	−	0.291587i	−0.122144	−	0.168117i	3.96988	−	7.79133i	−7.43957	−	14.6010i	12.8563	−	17.6952i		−	9.00000i	0.490029	+	0.356027i
43.8	−2.03759	+	0.662054i	2.12132	−	2.12132i	−2.75866	+	2.00429i	5.81614	+	8.00524i	−2.91796	+	5.72682i	2.98496	+	5.85832i	14.3685	−	19.7766i		−	9.00000i	−17.1508	−	12.4608i
43.9	−0.913878	+	0.296937i	2.12132	−	2.12132i	−5.72513	+	4.15955i	5.34202	+	7.35266i	−1.30873	+	2.56853i	−16.3859	−	32.1592i	8.51541	−	11.7205i		−	9.00000i	−7.06523	−	5.13319i
43.10	−0.807722	+	0.262445i	−2.12132	+	2.12132i	−5.88860	+	4.27832i	0.202575	+	0.278820i	1.15671	−	2.27017i	10.2772	+	20.1701i	7.62712	−	10.4978i		−	9.00000i	−0.236799	−	0.172044i
43.11	−0.379547	+	0.123322i	−2.12132	+	2.12132i	−6.34329	+	4.60867i	−3.94550	−	5.43051i	0.543534	−	1.06675i	−4.36592	−	8.56861i	3.71580	−	5.11437i		−	9.00000i	2.16720	+	1.57457i
43.12	−0.204548	+	0.0664617i	2.12132	−	2.12132i	−6.43471	+	4.67509i	−7.28724	−	10.0300i	−0.292925	+	0.574898i	14.8654	+	29.1751i	2.01683	−	2.77593i		−	9.00000i	2.15720	+	1.56730i
43.13	0.917910	−	0.298247i	−2.12132	+	2.12132i	−5.71853	+	4.15475i	12.0749	+	16.6197i	−1.31450	+	2.57986i	−12.9950	−	25.5042i	−8.54835	+	11.7658i		−	9.00000i	16.0405	+	11.6541i
43.14	1.07155	−	0.348167i	2.12132	−	2.12132i	−5.44514	+	3.95613i	−5.91570	−	8.14226i	1.53452	−	3.01167i	−4.18344	−	8.21046i	−9.75535	+	13.4271i		−	9.00000i	−9.17381	−	6.66516i
43.15	2.04260	−	0.663682i	2.12132	−	2.12132i	−2.74038	+	1.99101i	8.69597	+	11.9690i	2.92513	−	5.74090i	8.32183	+	16.3325i	−14.3753	+	19.7859i		−	9.00000i	25.7060	+	18.6765i
43.16	2.62903	−	0.854225i	−2.12132	+	2.12132i	−0.290013	+	0.210707i	−3.05341	−	4.20265i	−3.76494	+	7.38911i	12.8260	+	25.1725i	−13.5811	+	18.6928i		−	9.00000i	−11.6175	−	8.44062i
43.17	2.97740	−	0.967416i	−2.12132	+	2.12132i	1.45688	−	1.05849i	−7.64578	−	10.5235i	−4.26382	+	8.36822i	−11.1006	−	21.7862i	−11.4073	+	15.7009i		−	9.00000i	−32.9452	−	23.9361i
43.18	4.00859	−	1.30247i	2.12132	−	2.12132i	7.90024	−	5.73986i	−8.84506	−	12.1742i	5.74055	−	11.2665i	−5.78514	−	11.3540i	4.37328	−	6.01930i		−	9.00000i	−51.3127	−	37.2809i
43.19	4.13168	−	1.34247i	−2.12132	+	2.12132i	8.79647	−	6.39101i	8.45362	+	11.6354i	−5.91683	+	11.6124i	3.83164	+	7.52001i	7.33636	−	10.0976i		−	9.00000i	50.5478	+	36.7252i
43.20	4.25251	−	1.38172i	2.12132	−	2.12132i	9.70256	−	7.04932i	5.94448	+	8.18187i	6.08986	−	11.9520i	−7.25307	−	14.2350i	10.4944	−	14.4444i		−	9.00000i	36.5841	+	26.5799i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
41.g	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	123.4.n.a	✓	176
41.g	even	20	1	inner	123.4.n.a	✓	176

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
123.4.n.a	✓	176	1.a	even	1	1	trivial
123.4.n.a	✓	176	41.g	even	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(123, [\chi])\).