Newform orbit 92.6.h.a

• Label: 92.6.h.a
• Level: $92$
• Weight: $6$
• Character orbit: 92.h
• Analytic conductor: $14.755$
• Analytic rank: $0$
• Dimension: $580$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	92.h (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7553114228\)
Analytic rank:	\(0\)
Dimension:	\(580\)
Relative dimension:	\(58\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 580 q - 11 q^{2} - 51 q^{4} - 22 q^{5} - 310 q^{6} + 382 q^{8} + 4356 q^{9}+O(q^{10}) \)

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	−5.65279	−	0.214310i	14.6997	+	22.8732i	31.9081	+	2.42290i	31.4635	−	14.3689i	−78.1924	−	132.448i	−150.465	+	44.1806i	−179.851	−	20.5343i	−206.155	+	451.417i	−180.936	+	74.4814i
7.2	−5.64788	−	0.318447i	−7.84053	−	12.2001i	31.7972	+	3.59710i	−44.2428	+	20.2050i	40.3973	+	71.4016i	88.4924	−	25.9837i	−178.441	−	30.4417i	13.5772	−	29.7300i	256.312	−	100.026i
7.3	−5.63576	+	0.488107i	−1.52528	−	2.37339i	31.5235	−	5.50171i	97.4661	−	44.5113i	9.75459	+	12.6313i	160.103	−	47.0105i	−174.973	+	46.3932i	97.6394	−	213.800i	−527.569	+	298.429i
7.4	−5.60186	−	0.786860i	6.63092	+	10.3179i	30.7617	+	8.81576i	−87.3758	+	39.9032i	−29.0267	−	63.0171i	−57.2232	+	16.8022i	−165.386	−	73.5898i	38.4556	−	84.2061i	520.865	−	154.780i
7.5	−5.44026	+	1.55036i	−3.25011	−	5.05727i	27.1928	−	16.8687i	5.81507	−	2.65566i	25.5220	+	22.4740i	−132.403	+	38.8770i	−121.783	+	133.929i	85.9331	−	188.167i	−27.5183	+	23.4629i
7.6	−5.40659	−	1.66397i	−15.2234	−	23.6880i	26.4624	+	17.9928i	73.1065	−	33.3866i	42.8902	+	153.403i	−95.1302	+	27.9327i	−113.132	−	141.313i	−228.426	+	500.183i	−450.811	+	58.8605i
7.7	−5.34986	+	1.83821i	11.6058	+	18.0590i	25.2420	−	19.6683i	−36.6705	+	16.7469i	−95.2854	−	75.2790i	189.511	−	55.6454i	−98.8867	+	151.623i	−90.4857	+	198.136i	165.398	−	157.001i
7.8	−5.25220	−	2.10105i	−7.50050	−	11.6710i	23.1712	+	22.0702i	−19.2953	+	8.81189i	14.8728	+	77.0573i	94.5594	−	27.7651i	−75.3293	−	164.601i	20.9910	−	45.9639i	119.857	−	5.74139i
7.9	−5.17139	−	2.29275i	9.04824	+	14.0793i	21.4866	+	23.7134i	49.3323	−	22.5293i	−14.5116	−	93.5552i	151.099	−	44.3666i	−56.7464	−	171.895i	−15.4113	+	33.7460i	−306.771	+	3.40111i
7.10	−5.11541	+	2.41507i	−15.4609	−	24.0576i	20.3349	−	24.7082i	−42.0751	+	19.2150i	137.190	+	85.7255i	−48.6242	+	14.2774i	−44.3492	+	175.503i	−238.784	+	522.865i	168.826	−	199.907i
7.11	−4.87176	−	2.87506i	0.137319	+	0.213673i	15.4681	+	28.0132i	48.9663	−	22.3621i	−0.0546636	−	1.43576i	−228.032	+	66.9562i	5.18301	−	180.945i	100.919	−	220.982i	−302.844	−	31.8380i
7.12	−4.75071	+	3.07095i	5.81565	+	9.04932i	13.1385	−	29.1784i	18.2402	−	8.33002i	−55.4185	−	25.1312i	39.7249	−	11.6643i	27.1882	+	178.966i	52.8773	−	115.785i	−61.0729	+	95.5883i
7.13	−4.41315	−	3.53894i	6.01463	+	9.35895i	6.95176	+	31.2358i	−20.0029	+	9.13500i	6.57733	−	62.5879i	40.7135	−	11.9546i	79.8625	−	162.450i	49.5317	−	108.459i	120.604	+	30.4749i
7.14	−3.93295	+	4.06595i	−11.0031	−	17.1211i	−1.06385	−	31.9823i	66.1029	−	30.1882i	112.888	+	22.5985i	74.3441	−	21.8294i	134.222	+	121.459i	−71.1192	+	155.729i	−137.236	+	387.499i
7.15	−3.76159	+	4.22498i	−5.43070	−	8.45033i	−3.70093	−	31.7853i	−80.0209	+	36.5443i	56.1305	+	8.84206i	198.579	−	58.3082i	148.214	+	103.927i	59.0302	−	129.258i	146.606	−	475.551i
7.16	−3.64665	+	4.32458i	5.43070	+	8.45033i	−5.40393	−	31.5404i	−80.0209	+	36.5443i	−56.3480	−	7.32991i	−198.579	+	58.3082i	156.105	+	91.6471i	59.0302	−	129.258i	133.769	−	479.321i
7.17	−3.62873	−	4.33962i	−10.5572	−	16.4274i	−5.66460	+	31.4946i	−89.9184	+	41.0643i	−32.9792	+	105.425i	−150.422	+	44.1680i	157.230	−	89.7034i	−57.4573	+	125.814i	504.493	+	241.200i
7.18	−3.46484	+	4.47156i	11.0031	+	17.1211i	−7.98970	−	30.9865i	66.1029	−	30.1882i	−114.682	−	10.1211i	−74.3441	+	21.8294i	166.241	+	71.6370i	−71.1192	+	155.729i	−94.0480	+	400.180i
7.19	−3.28600	−	4.60459i	−13.1025	−	20.3878i	−10.4045	+	30.2613i	13.6959	−	6.25472i	−50.8229	+	127.326i	185.138	−	54.3614i	173.530	−	51.5303i	−143.043	+	313.221i	−73.8051	−	42.5111i
7.20	−2.93634	−	4.83507i	14.5445	+	22.6317i	−14.7558	+	28.3948i	−58.7945	+	26.8506i	66.7183	−	136.778i	−52.5573	+	15.4322i	180.619	−	12.0311i	−199.705	+	437.293i	302.465	+	205.434i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.d	odd	22	1	inner
92.h	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.6.h.a	✓	580
4.b	odd	2	1	inner	92.6.h.a	✓	580
23.d	odd	22	1	inner	92.6.h.a	✓	580
92.h	even	22	1	inner	92.6.h.a	✓	580

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.6.h.a	✓	580	1.a	even	1	1	trivial
92.6.h.a	✓	580	4.b	odd	2	1	inner
92.6.h.a	✓	580	23.d	odd	22	1	inner
92.6.h.a	✓	580	92.h	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(92, [\chi])\).