Newform orbit 100.7.j.a

• Label: 100.7.j.a
• Level: $100$
• Weight: $7$
• Character orbit: 100.j
• Analytic conductor: $23.005$
• Analytic rank: $0$
• Dimension: $352$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.0054083620\)
Analytic rank:	\(0\)
Dimension:	\(352\)
Relative dimension:	\(88\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 352 q - 3 q^{2} - 3 q^{4} - 30 q^{5} - 131 q^{6} - 1452 q^{8} + 20406 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−7.99909	−	0.120477i	46.4131	+	15.0805i	63.9710	+	1.92742i	−46.8990	+	115.868i	−369.446	−	126.222i		−	404.030i	−511.478	−	23.1246i	1336.98	+	971.375i	389.109	−	921.192i
11.2	−7.99000	+	0.399973i	16.1811	+	5.25755i	63.6800	−	6.39156i	102.065	+	72.1645i	−131.390	−	35.5358i		−	250.062i	−506.247	+	76.5389i	−355.588	−	258.350i	−844.363	−	535.771i
11.3	−7.97744	−	0.600412i	38.6093	+	12.5449i	63.2790	+	9.57950i	67.2413	−	105.374i	−300.471	−	123.258i			253.746i	−499.053	−	114.413i	743.527	+	540.204i	−599.681	+	800.239i
11.4	−7.95545	−	0.843087i	−26.0644	−	8.46884i	62.5784	+	13.4143i	41.9765	+	117.741i	200.214	+	89.3480i			407.454i	−486.530	−	159.476i	17.8594	+	12.9756i	−234.676	−	972.074i
11.5	−7.94483	−	0.937884i	−27.5098	−	8.93849i	62.2407	+	14.9027i	−119.369	−	37.0937i	210.178	+	96.8158i			272.022i	−480.515	−	176.774i	87.1208	+	63.2970i	913.581	+	406.658i
11.6	−7.88737	+	1.33770i	−5.70970	−	1.85519i	60.4211	−	21.1019i	−28.4725	−	121.714i	47.5162	+	6.99472i		−	641.481i	−448.335	+	247.264i	−560.614	−	407.310i	387.390	+	921.916i
11.7	−7.85582	+	1.51197i	−42.8387	−	13.9191i	59.4279	−	23.7555i	−61.7464	+	108.685i	357.578	+	44.5754i		−	147.470i	−430.937	+	276.473i	1051.64	+	764.058i	320.741	−	947.167i
11.8	−7.85233	−	1.53002i	−42.7655	−	13.8953i	59.3181	+	24.0284i	118.669	−	39.2772i	314.548	+	174.543i		−	604.413i	−429.021	−	279.437i	1046.03	+	759.987i	−991.922	+	126.852i
11.9	−7.77128	+	1.89928i	−3.71928	−	1.20847i	56.7855	−	29.5196i	41.5490	−	117.893i	31.1987	+	2.32738i			393.890i	−385.230	+	337.257i	−577.401	−	419.506i	−98.9778	+	995.090i
11.10	−7.63717	−	2.38194i	29.2274	+	9.49655i	52.6528	+	36.3825i	−124.997	+	0.875078i	−200.594	−	142.144i			560.883i	−315.457	−	403.275i	174.281	+	126.623i	956.707	+	291.052i
11.11	−7.62116	+	2.43269i	7.40147	+	2.40488i	52.1641	−	37.0798i	−120.466	+	33.3609i	−62.2581	−	0.322533i		−	75.1439i	−307.347	+	409.490i	−540.775	−	392.896i	836.933	−	547.305i
11.12	−7.46526	−	2.87575i	3.13093	+	1.01730i	47.4601	+	42.9365i	124.893	−	5.17667i	−20.4477	−	16.5982i			36.1548i	−230.827	−	457.015i	−581.006	−	422.125i	−947.243	−	320.516i
11.13	−6.97959	−	3.90964i	22.7842	+	7.40305i	33.4294	+	54.5754i	−92.5214	−	84.0523i	−130.082	−	140.748i		−	380.818i	−19.9537	−	511.611i	−125.457	−	91.1495i	317.147	+	948.376i
11.14	−6.94115	+	3.97749i	18.8992	+	6.14073i	32.3592	−	55.2167i	18.1114	+	123.681i	−155.607	+	32.5477i			535.870i	−4.98613	+	511.976i	−270.302	−	196.386i	−617.653	−	786.451i
11.15	−6.87030	−	4.09865i	−27.5146	−	8.94005i	30.4022	+	56.3179i	3.10817	−	124.961i	152.392	+	174.194i			154.008i	21.9554	−	511.529i	87.3574	+	63.4689i	−533.527	+	845.783i
11.16	−6.85958	+	4.11658i	−30.8650	−	10.0286i	30.1076	−	56.4759i	124.132	−	14.7020i	253.004	−	58.2657i			190.767i	25.9620	+	511.341i	262.298	+	190.571i	−790.974	+	611.850i
11.17	−6.81886	−	4.18367i	−6.26689	−	2.03624i	28.9938	+	57.0558i	−50.4045	+	114.387i	34.2141	+	40.1034i		−	242.667i	40.9979	−	510.356i	−554.646	−	402.974i	822.259	−	569.114i
11.18	−6.65794	+	4.43529i	41.0804	+	13.3478i	24.6564	−	59.0598i	−80.0267	−	96.0246i	−332.713	+	93.3344i		−	38.3621i	97.7865	+	502.575i	919.662	+	668.174i	958.710	+	284.385i
11.19	−6.27563	+	4.96150i	−41.0804	−	13.3478i	14.7670	−	62.2731i	−80.0267	−	96.0246i	324.031	−	120.054i			38.3621i	216.295	+	464.069i	919.662	+	668.174i	978.644	+	205.563i
11.20	−6.03482	+	5.25175i	30.8650	+	10.0286i	8.83816	−	63.3868i	124.132	−	14.7020i	−238.932	+	101.574i		−	190.767i	279.555	+	428.944i	262.298	+	190.571i	−671.905	+	740.637i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
25.d	even	5	1	inner
100.j	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	100.7.j.a	✓	352
4.b	odd	2	1	inner	100.7.j.a	✓	352
25.d	even	5	1	inner	100.7.j.a	✓	352
100.j	odd	10	1	inner	100.7.j.a	✓	352

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
100.7.j.a	✓	352	1.a	even	1	1	trivial
100.7.j.a	✓	352	4.b	odd	2	1	inner
100.7.j.a	✓	352	25.d	even	5	1	inner
100.7.j.a	✓	352	100.j	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(100, [\chi])\).