Newform orbit 92.7.g.a

• Label: 92.7.g.a
• Level: $92$
• Weight: $7$
• Character orbit: 92.g
• Analytic conductor: $21.165$
• Analytic rank: $0$
• Dimension: $700$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(21.1649756930\)
Analytic rank:	\(0\)
Dimension:	\(700\)
Relative dimension:	\(70\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 700 q - 19 q^{2} + 213 q^{4} - 18 q^{5} - 716 q^{6} + 296 q^{8} + 16020 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−7.99595	+	0.254408i	−35.2437	−	16.0953i	63.8706	−	4.06848i	−93.7314	+	108.172i	285.902	+	119.731i	−96.1156	−	149.559i	−509.671	+	48.7805i	505.669	+	583.573i	721.952	−	888.783i
3.2	−7.98923	−	0.414919i	5.28949	+	2.41563i	63.6557	+	6.62977i	−89.9605	+	103.820i	−41.2567	−	21.4937i	−27.5706	−	42.9007i	−505.809	−	79.3787i	−455.250	−	525.387i	761.792	−	792.115i
3.3	−7.97011	+	0.690905i	−14.8069	−	6.76209i	63.0453	−	11.0132i	31.8755	−	36.7863i	122.685	+	43.6644i	333.694	+	519.238i	−494.869	+	131.335i	−303.875	−	350.690i	−228.635	+	315.214i
3.4	−7.81125	+	1.72753i	3.08319	+	1.40805i	58.0313	−	26.9884i	80.7139	−	93.1488i	−26.5160	−	5.67230i	−230.140	−	358.104i	−406.674	+	311.064i	−469.870	−	542.259i	−469.559	+	867.044i
3.5	−7.81069	−	1.73008i	46.2230	+	21.1093i	58.0136	+	27.0263i	−58.3545	+	67.3447i	−324.512	−	244.848i	−227.243	−	353.597i	−406.368	−	311.462i	1213.57	+	1400.53i	572.301	−	425.050i
3.6	−7.80798	+	1.74224i	42.3500	+	19.3406i	57.9292	−	27.2068i	147.463	−	170.181i	−364.364	−	77.2270i	249.749	+	388.617i	−404.909	+	313.357i	942.071	+	1087.21i	−854.889	+	1585.69i
3.7	−7.63590	+	2.38600i	31.0638	+	14.1864i	52.6140	−	36.4385i	−137.283	+	158.433i	−271.049	−	34.2075i	246.827	+	384.070i	−314.813	+	403.778i	286.316	+	330.426i	670.256	−	1537.33i
3.8	−7.60199	−	2.49194i	−38.4440	−	17.5568i	51.5804	+	37.8874i	60.5396	−	69.8665i	248.501	+	229.267i	−47.2214	−	73.4779i	−297.701	−	416.555i	692.309	+	798.967i	−634.325	+	380.263i
3.9	−7.57935	−	2.55997i	22.0421	+	10.0663i	50.8931	+	38.8059i	44.2549	−	51.0729i	−141.295	−	132.723i	19.1193	+	29.7502i	−286.394	−	424.408i	−92.8700	−	107.178i	−466.168	+	273.808i
3.10	−6.99391	−	3.88396i	−13.1021	−	5.98354i	33.8296	+	54.3282i	139.591	−	161.097i	68.3952	+	92.7365i	−14.9410	−	23.2487i	−25.5928	−	511.360i	−341.531	−	394.147i	−1601.98	+	584.530i
3.11	−6.96219	+	3.94055i	−42.7903	−	19.5417i	32.9441	−	54.8697i	99.7035	−	115.064i	374.919	−	32.5645i	−71.7386	−	111.627i	−13.1465	+	511.831i	971.742	+	1121.45i	−240.739	+	1193.98i
3.12	−6.72156	+	4.33827i	27.3171	+	12.4753i	26.3588	−	58.3199i	7.53569	−	8.69665i	−237.735	+	34.6555i	−108.050	−	168.129i	75.8355	+	506.353i	113.198	+	130.637i	−12.9232	+	91.1469i
3.13	−6.55848	−	4.58109i	24.1439	+	11.0262i	22.0273	+	60.0899i	−23.1933	+	26.7665i	−107.836	−	182.920i	220.588	+	343.241i	130.812	−	495.007i	−16.0408	−	18.5121i	274.733	−	69.2971i
3.14	−6.50324	+	4.65917i	−21.1292	−	9.64940i	20.5843	−	60.5994i	−106.997	+	123.481i	182.367	−	35.6924i	−171.532	−	266.909i	148.479	+	489.998i	−124.059	−	143.172i	120.507	−	1301.54i
3.15	−6.48182	−	4.68893i	−3.09024	−	1.41127i	20.0279	+	60.7855i	−96.3722	+	111.220i	13.4131	+	23.6375i	−175.226	−	272.657i	155.202	−	487.910i	−469.836	−	542.219i	1146.17	−	269.022i
3.16	−6.44354	+	4.74139i	−25.8713	−	11.8150i	19.0385	−	61.1027i	44.0755	−	50.8658i	222.722	−	46.5352i	183.646	+	285.758i	167.036	+	483.987i	52.3358	+	60.3987i	−42.8277	+	536.735i
3.17	−6.17262	−	5.08908i	−30.4093	−	13.8875i	12.2025	+	62.8259i	−89.7403	+	103.566i	117.031	+	240.478i	263.513	+	410.035i	244.404	−	449.901i	254.471	+	293.676i	1080.99	−	182.577i
3.18	−5.82057	+	5.48826i	1.99428	+	0.910758i	3.75801	−	63.8896i	−64.7370	+	74.7105i	−16.6063	+	5.64401i	164.365	+	255.757i	328.769	+	392.498i	−474.246	−	547.309i	−33.2245	−	790.151i
3.19	−5.32270	−	5.97235i	−12.8149	−	5.85236i	−7.33783	+	63.5780i	−16.2506	+	18.7542i	33.2574	+	107.685i	−344.320	−	535.773i	418.767	−	294.582i	−347.422	−	400.947i	198.503	−	2.76864i
3.20	−4.95618	+	6.27983i	39.8929	+	18.2185i	−14.8725	−	62.2480i	−16.6352	+	19.1980i	−312.125	+	160.227i	−153.863	−	239.416i	464.618	+	215.115i	782.137	+	902.634i	−38.1133	−	199.615i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.c	even	11	1	inner
92.g	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.7.g.a	✓	700
4.b	odd	2	1	inner	92.7.g.a	✓	700
23.c	even	11	1	inner	92.7.g.a	✓	700
92.g	odd	22	1	inner	92.7.g.a	✓	700

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.7.g.a	✓	700	1.a	even	1	1	trivial
92.7.g.a	✓	700	4.b	odd	2	1	inner
92.7.g.a	✓	700	23.c	even	11	1	inner
92.7.g.a	✓	700	92.g	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(92, [\chi])\).