Newform orbit 124.5.n.a

• Label: 124.5.n.a
• Level: $124$
• Weight: $5$
• Character orbit: 124.n
• Analytic conductor: $12.818$
• Analytic rank: $0$
• Dimension: $496$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.n (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.8178754224\)
Analytic rank:	\(0\)
Dimension:	\(496\)
Relative dimension:	\(62\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 496 q - 6 q^{2} + 22 q^{4} - 8 q^{5} - 5 q^{6} + 93 q^{8} - 1584 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−3.99981	+	0.0388022i	−2.44081	−	11.4831i	15.9970	−	0.310403i	6.58787	−	11.4105i	10.2083	+	45.8355i	−18.4874	+	41.5235i	−63.9729	+	1.86227i	−51.9070	+	23.1105i	−25.9075	+	45.8956i
7.2	−3.99553	+	0.188984i	−2.23799	−	10.5289i	15.9286	−	1.51018i	−13.0823	+	22.6592i	10.9318	+	41.6457i	22.2829	−	50.0481i	−63.3577	+	9.04421i	−31.8522	+	14.1815i	47.9886	−	93.0081i
7.3	−3.96139	−	0.554462i	1.57807	+	7.42425i	15.3851	+	4.39288i	15.1333	−	26.2116i	−2.13489	−	30.2853i	9.79025	−	21.9893i	−58.5108	−	25.9323i	21.3681	−	9.51368i	−74.4821	+	95.4435i
7.4	−3.95268	+	0.613468i	3.60409	+	16.9559i	15.2473	−	4.84968i	−17.9457	+	31.0829i	−24.6477	−	64.8102i	23.8950	−	53.6691i	−57.2926	+	28.5230i	−200.516	+	89.2754i	51.8652	−	133.870i
7.5	−3.86289	+	1.03830i	0.985100	+	4.63453i	13.8439	−	8.02168i	0.495508	−	0.858245i	−8.61737	−	16.8799i	−6.76944	+	15.2044i	−45.1484	+	45.3610i	53.4887	−	23.8147i	−1.02298	+	3.82979i
7.6	−3.84350	−	1.10792i	2.94372	+	13.8491i	13.5450	+	8.51658i	0.710866	−	1.23126i	4.02950	−	56.4906i	−35.5461	+	79.8379i	−42.6247	−	47.7403i	−109.136	+	48.5903i	−4.09635	+	3.94475i
7.7	−3.73148	−	1.44085i	0.102585	+	0.482623i	11.8479	+	10.7530i	−13.3531	+	23.1282i	0.312593	−	1.94871i	26.5552	−	59.6440i	−28.7169	−	57.1956i	73.7748	−	32.8466i	83.1509	−	67.0627i
7.8	−3.69586	−	1.52990i	−1.10506	−	5.19888i	11.3188	+	11.3086i	22.8055	−	39.5003i	−3.86963	+	20.9050i	1.82641	−	4.10218i	−24.5317	−	59.1117i	48.1900	−	21.4556i	−144.718	+	111.098i
7.9	−3.61454	−	1.71320i	−1.01116	−	4.75715i	10.1299	+	12.3849i	−19.2833	+	33.3997i	−4.49507	+	18.9273i	−32.9145	+	73.9271i	−15.3970	−	62.1203i	52.3892	−	23.3252i	126.921	−	87.6883i
7.10	−3.44339	+	2.03546i	0.663541	+	3.12172i	7.71382	−	14.0177i	−20.6641	+	35.7913i	−8.63895	−	9.39866i	−17.0748	+	38.3507i	1.97083	+	63.9696i	64.6924	−	28.8029i	−1.69713	−	165.304i
7.11	−3.38631	+	2.12906i	−1.09964	−	5.17342i	6.93422	−	14.4193i	13.8083	−	23.9166i	14.7383	+	15.1776i	27.0372	−	60.7265i	7.21815	+	63.5917i	48.4421	−	21.5678i	4.16079	+	110.388i
7.12	−3.32566	−	2.22261i	1.74446	+	8.20705i	6.12005	+	14.7833i	−3.81582	+	6.60919i	12.4395	−	31.1711i	7.60990	−	17.0921i	12.5042	−	62.7666i	9.68470	−	4.31191i	27.3798	−	13.4989i
7.13	−3.20374	+	2.39500i	3.07870	+	14.4841i	4.52794	−	15.3459i	19.0680	−	33.0268i	−44.5529	−	39.0300i	−3.74892	+	8.42020i	22.2472	+	60.0089i	−126.315	+	56.2389i	18.0101	+	151.477i
7.14	−3.16751	−	2.44273i	−3.46609	−	16.3067i	4.06618	+	15.4747i	6.20373	−	10.7452i	−28.8539	+	60.1182i	23.6810	−	53.1885i	24.9208	−	58.9487i	−179.897	+	80.0951i	−45.8979	+	18.8814i
7.15	−3.09063	+	2.53930i	−3.26760	−	15.3728i	3.10393	−	15.6960i	−9.65087	+	16.7158i	49.1352	+	39.2143i	−8.10859	+	18.2122i	30.2638	+	56.3924i	−151.650	+	67.5190i	−12.6192	−	76.1687i
7.16	−2.70980	+	2.94228i	−1.29821	−	6.10758i	−1.31401	−	15.9460i	14.4130	−	24.9640i	21.4881	+	12.7306i	−37.8130	+	84.9295i	50.4782	+	39.3441i	38.3800	−	17.0879i	34.3949	+	110.054i
7.17	−2.59129	−	3.04716i	−2.19097	−	10.3077i	−2.57041	+	15.7922i	−1.15616	+	2.00253i	−25.7318	+	33.3866i	−17.9261	+	40.2628i	54.7820	−	33.0897i	−27.4515	+	12.2222i	9.09800	−	1.66613i
7.18	−2.30380	−	3.26994i	3.28358	+	15.4480i	−5.38502	+	15.0666i	16.1223	−	27.9247i	42.9494	−	46.3262i	25.8674	−	58.0991i	61.6728	−	17.1016i	−153.862	+	68.5038i	−128.455	+	11.6138i
7.19	−2.21932	+	3.32785i	1.76732	+	8.31457i	−6.14921	−	14.7712i	−7.19445	+	12.4612i	−31.5919	−	12.5713i	34.2185	−	76.8560i	62.8033	+	12.3183i	7.98859	−	3.55675i	−25.5021	−	51.5974i
7.20	−2.17905	−	3.35436i	−0.564139	−	2.65406i	−6.50348	+	14.6186i	0.850733	−	1.47351i	−7.67340	+	7.67567i	12.2724	−	27.5642i	63.2076	−	10.0397i	67.2714	−	29.9511i	−6.79648	+	0.357193i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.g	even	15	1	inner
124.n	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.5.n.a	✓	496
4.b	odd	2	1	inner	124.5.n.a	✓	496
31.g	even	15	1	inner	124.5.n.a	✓	496
124.n	odd	30	1	inner	124.5.n.a	✓	496

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.5.n.a	✓	496	1.a	even	1	1	trivial
124.5.n.a	✓	496	4.b	odd	2	1	inner
124.5.n.a	✓	496	31.g	even	15	1	inner
124.5.n.a	✓	496	124.n	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(124, [\chi])\).