Newform orbit 83.12.c.a

• Label: 83.12.c.a
• Level: $83$
• Weight: $12$
• Character orbit: 83.c
• Analytic conductor: $63.772$
• Analytic rank: $0$
• Dimension: $3040$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	83.c (of order \(41\), degree \(40\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(63.7724839864\)
Analytic rank:	\(0\)
Dimension:	\(3040\)
Relative dimension:	\(76\) over \(\Q(\zeta_{41})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{41}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3040 q - 71 q^{2} - 565 q^{3} - 72883 q^{4} - 1227 q^{5} - 18299 q^{6} - 6897 q^{7} - 94247 q^{8} - 3940087 q^{9}+O(q^{10}) \)

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	−82.5647	+	33.2766i	−255.025	−	210.318i	4233.97	−	4074.79i	6962.86	−	9134.41i	28054.7	+	8878.45i	2651.69	+	203.582i	−139404.	+	310967.i	−12922.9	−	66634.2i	−270924.	+	985880.i
3.2	−79.4299	+	32.0131i	443.034	+	365.367i	3808.64	−	3665.45i	−1949.18	+	2557.08i	−46886.7	−	14838.2i	86332.2	+	6628.12i	−113432.	+	253031.i	29058.5	+	149834.i	72962.8	−	265508.i
3.3	−78.8256	+	31.7696i	−399.475	−	329.444i	3728.54	−	3588.36i	−5412.90	+	7101.05i	41955.1	+	13277.5i	65285.5	+	5012.26i	−108704.	+	242484.i	17319.2	+	89302.5i	201077.	−	731710.i
3.4	−78.6720	+	31.7077i	270.334	+	222.943i	3708.28	−	3568.86i	−7428.24	+	9744.93i	−28336.8	−	8967.71i	−53852.2	−	4134.48i	−107517.	+	239836.i	−10350.2	−	53368.2i	275405.	−	1.00219e6i
3.5	−76.9205	+	31.0018i	18.4044	+	15.1780i	3480.03	−	3349.20i	657.194	−	862.157i	−1886.22	−	596.930i	548.121	+	42.0817i	−94376.0	+	210523.i	−33618.9	−	173348.i	−23823.3	+	86691.8i
3.6	−75.3819	+	30.3816i	−585.883	−	483.174i	3283.76	−	3160.30i	458.286	−	601.215i	58844.6	+	18622.5i	−69652.8	−	5347.56i	−83431.6	+	186110.i	76074.4	+	392260.i	−16280.6	+	59244.2i
3.7	−74.6244	+	30.0763i	348.490	+	287.397i	3188.59	−	3068.71i	1266.98	−	1662.12i	−34649.7	−	10965.6i	−47576.4	−	3652.66i	−78246.1	+	174542.i	5120.58	+	26403.1i	−44557.1	+	162141.i
3.8	−73.8081	+	29.7473i	481.162	+	396.811i	3087.10	−	2971.04i	7827.67	−	10268.9i	−47317.7	−	14974.6i	6415.38	+	492.538i	−72805.1	+	162405.i	40330.3	+	207954.i	−272272.	+	990783.i
3.9	−68.5514	+	27.6287i	−420.862	−	347.083i	2460.32	−	2367.82i	−5474.44	+	7181.79i	38440.1	+	12165.1i	−4553.74	−	349.611i	−41319.0	+	92169.7i	22931.6	+	118241.i	176857.	−	643573.i
3.10	−68.4587	+	27.5913i	−146.605	−	120.904i	2449.68	−	2357.58i	−1208.45	+	1585.33i	13372.3	+	4231.93i	−24415.4	−	1874.48i	−40817.3	+	91050.5i	−26852.0	−	138456.i	38987.2	−	141872.i
3.11	−64.2079	+	25.8781i	−479.144	−	395.147i	1977.35	−	1903.01i	4518.01	−	5927.08i	40990.5	+	12972.2i	56410.7	+	4330.91i	−19719.1	+	43987.2i	39710.4	+	204758.i	−136711.	+	497483.i
3.12	−60.9306	+	24.5572i	616.129	+	508.118i	1633.85	−	1572.42i	457.204	−	599.795i	−50019.1	−	15829.5i	−60651.2	−	4656.47i	−5901.19	+	13163.7i	87703.9	+	452225.i	−13128.4	+	47773.5i
3.13	−60.0474	+	24.2013i	−173.347	−	142.958i	1544.36	−	1486.30i	4433.38	−	5816.05i	13868.8	+	4389.05i	57782.7	+	4436.24i	−2526.42	+	5635.66i	−24115.1	−	124344.i	−125457.	+	456533.i
3.14	−59.5949	+	24.0189i	308.558	+	254.466i	1499.02	−	1442.66i	1800.52	−	2362.05i	−24500.5	−	7753.64i	31948.8	+	2452.85i	−853.274	+	1903.39i	−3272.16	−	16872.1i	−50567.6	+	184013.i
3.15	−57.5847	+	23.2087i	538.298	+	443.931i	1301.72	−	1252.78i	−5538.09	+	7265.29i	−41300.7	−	13070.4i	18703.4	+	1435.94i	6129.95	−	13674.0i	58962.5	+	304027.i	150291.	−	546901.i
3.16	−56.6723	+	22.8410i	−173.792	−	143.326i	1214.41	−	1168.76i	7272.56	−	9540.70i	13122.9	+	4153.00i	−83780.0	−	6432.17i	9061.55	−	20213.5i	−24065.6	−	124089.i	−194234.	+	706807.i
3.17	−56.5254	+	22.7818i	25.4399	+	20.9801i	1200.49	−	1155.35i	−5236.54	+	6869.70i	−1915.97	−	606.345i	59950.5	+	4602.67i	9519.96	−	21236.1i	−33520.2	−	172839.i	139494.	−	507611.i
3.18	−52.3739	+	21.1086i	−565.452	−	466.325i	821.826	−	790.928i	3072.65	−	4030.94i	39458.4	+	12487.4i	9179.09	+	704.720i	20960.2	−	46755.6i	68549.8	+	353461.i	−75839.3	+	275975.i
3.19	−50.4608	+	20.3375i	86.5296	+	71.3604i	657.051	−	632.349i	2462.13	−	3230.01i	−5817.65	−	1841.11i	−49262.5	−	3782.10i	25284.1	−	56400.9i	−31332.2	−	161557.i	−58550.6	+	213063.i
3.20	−47.1098	+	18.9870i	162.641	+	134.129i	383.203	−	368.796i	−6214.36	+	8152.47i	−10208.7	−	3230.73i	−38026.0	−	2919.43i	31501.9	−	70270.9i	−25265.8	−	130277.i	137967.	−	502053.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
83.c	even	41	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	83.12.c.a	✓	3040
83.c	even	41	1	inner	83.12.c.a	✓	3040

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
83.12.c.a	✓	3040	1.a	even	1	1	trivial
83.12.c.a	✓	3040	83.c	even	41	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{12}^{\mathrm{new}}(83, [\chi])\).