Newform orbit 124.4.j.a

• Label: 124.4.j.a
• Level: $124$
• Weight: $4$
• Character orbit: 124.j
• Analytic conductor: $7.316$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.31623684071\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 3 q^{2} - 15 q^{4} - 16 q^{5} - 15 q^{8} - 384 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
15.1	−2.82840	−	0.0132683i	7.87115	+	5.71872i	7.99965	+	0.0750562i	−13.1003			−22.1869	−	16.2793i	25.7893	+	8.37945i	−22.6252	−	0.318431i	20.9077	+	64.3474i	37.0530	+	0.173820i
15.2	−2.81316	−	0.293474i	0.939320	+	0.682456i	7.82775	+	1.65118i	16.2568			−2.44218	−	2.19552i	15.2434	+	4.95289i	−21.5361	−	6.94228i	−7.92688	−	24.3964i	−45.7331	−	4.77097i
15.3	−2.75945	+	0.620848i	2.96859	+	2.15681i	7.22910	−	3.42639i	−2.68692			−9.53072	−	4.10855i	−18.6273	−	6.05236i	−17.8210	+	13.9431i	−4.18275	−	12.8732i	7.41440	−	1.66817i
15.4	−2.72510	+	0.757503i	−3.17557	−	2.30719i	6.85238	−	4.12855i	−16.6602			10.4015	+	3.88182i	−3.04000	−	0.987756i	−15.5460	+	16.4414i	−3.58232	−	11.0253i	45.4007	−	12.6201i
15.5	−2.70634	−	0.822040i	−5.26813	−	3.82752i	6.64850	+	4.44943i	9.59704			11.1109	+	14.6892i	−30.4915	−	9.90729i	−14.3355	−	17.5070i	4.75980	+	14.6492i	−25.9728	−	7.88915i
15.6	−2.63900	+	1.01768i	−7.46913	−	5.42664i	5.92867	−	5.37130i	5.42895			25.2336	+	6.71977i	16.7763	+	5.45096i	−10.1795	+	20.2083i	17.9960	+	55.3861i	−14.3270	+	5.52491i
15.7	−2.61727	−	1.07234i	−2.61926	−	1.90300i	5.70016	+	5.61321i	−5.30736			4.81463	+	7.78942i	21.9191	+	7.12195i	−8.89956	−	20.8038i	−5.10436	−	15.7096i	13.8908	+	5.69130i
15.8	−2.48461	−	1.35157i	3.71840	+	2.70158i	4.34653	+	6.71623i	−7.20285			−5.58740	−	11.7380i	−18.8171	−	6.11405i	−1.72198	−	22.5618i	−1.81547	−	5.58743i	17.8962	+	9.73514i
15.9	−2.41107	+	1.47877i	3.63646	+	2.64204i	3.62648	−	7.13083i	11.6709			−12.6747	−	0.992650i	10.8099	+	3.51236i	1.80118	+	22.5556i	−2.10001	−	6.46315i	−28.1393	+	17.2586i
15.10	−2.16768	−	1.81692i	6.84261	+	4.97145i	1.39764	+	7.87697i	15.5435			−5.79986	−	23.2089i	2.17443	+	0.706516i	11.2822	−	19.6141i	13.7626	+	42.3568i	−33.6933	−	28.2412i
15.11	−2.15145	+	1.83609i	−3.63646	−	2.64204i	1.25751	−	7.90055i	11.6709			12.6747	−	0.992650i	−10.8099	−	3.51236i	11.8007	+	19.3066i	−2.10001	−	6.46315i	−25.1094	+	21.4289i
15.12	−1.78541	−	2.19370i	−5.33512	−	3.87619i	−1.62460	+	7.83331i	−18.0276			1.02221	+	18.6242i	−11.4547	−	3.72185i	20.0845	−	10.4218i	5.09519	+	15.6814i	32.1868	+	39.5472i
15.13	−1.78336	+	2.19536i	7.46913	+	5.42664i	−1.63923	−	7.83026i	5.42895			−25.2336	+	6.71977i	−16.7763	−	5.45096i	20.1136	+	10.3655i	17.9960	+	55.3861i	−9.68179	+	11.9185i
15.14	−1.75505	−	2.21806i	3.06772	+	2.22883i	−1.83962	+	7.78562i	−5.95936			−0.440306	−	10.7161i	2.34935	+	0.763351i	20.4976	−	9.58373i	−3.90024	−	12.0037i	10.4590	+	13.2182i
15.15	−1.60159	−	2.33129i	−7.03574	−	5.11177i	−2.86983	+	7.46754i	11.4470			−0.648641	+	24.5893i	19.7410	+	6.41424i	22.0053	−	5.26953i	15.0281	+	46.2517i	−18.3334	−	26.6862i
15.16	−1.56253	+	2.35765i	3.17557	+	2.30719i	−3.11699	−	7.36779i	−16.6602			−10.4015	+	3.88182i	3.04000	+	0.987756i	22.2410	+	4.16365i	−3.58232	−	11.0253i	26.0321	−	39.2788i
15.17	−1.44318	+	2.43254i	−2.96859	−	2.15681i	−3.83448	−	7.02117i	−2.68692			9.53072	−	4.10855i	18.6273	+	6.05236i	22.6131	+	0.805281i	−4.18275	−	12.8732i	3.87770	−	6.53602i
15.18	−1.11434	−	2.59966i	−0.687892	−	0.499783i	−5.51648	+	5.79383i	12.6815			−0.532718	+	2.34522i	−14.1641	−	4.60220i	21.2093	+	7.88465i	−8.12005	−	24.9909i	−14.1316	−	32.9677i
15.19	−0.861403	+	2.69406i	−7.87115	−	5.71872i	−6.51597	−	4.64135i	−13.1003			22.1869	−	16.2793i	−25.7893	−	8.37945i	18.1170	−	13.5564i	20.9077	+	64.3474i	11.2847	−	35.2932i
15.20	−0.618335	−	2.76001i	2.24034	+	1.62770i	−7.23532	+	3.41322i	−9.14807			3.10720	−	7.18983i	31.6620	+	10.2876i	13.8944	+	17.8591i	−5.97375	−	18.3853i	5.65657	+	25.2488i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.f	odd	10	1	inner
124.j	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.4.j.a	✓	184
4.b	odd	2	1	inner	124.4.j.a	✓	184
31.f	odd	10	1	inner	124.4.j.a	✓	184
124.j	even	10	1	inner	124.4.j.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.4.j.a	✓	184	1.a	even	1	1	trivial
124.4.j.a	✓	184	4.b	odd	2	1	inner
124.4.j.a	✓	184	31.f	odd	10	1	inner
124.4.j.a	✓	184	124.j	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(124, [\chi])\).