Newform orbit 19.10.c.a

• Label: 19.10.c.a
• Level: $19$
• Weight: $10$
• Character orbit: 19.c
• Analytic conductor: $9.786$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.78568088711\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9}+O(q^{10}) \)

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	−19.9646	−	34.5797i	53.5081	+	92.6787i	−541.171	+	937.336i	−90.9465	−	157.524i	2136.54	−	3700.59i	6421.38			22773.3			4115.27	−	7127.85i	−3631.42	+	6289.81i
7.2	−17.0666	−	29.5602i	−104.220	−	180.515i	−326.535	+	565.575i	1253.36	+	2170.89i	−3557.37	+	6161.54i	4067.64			4815.16			−11882.3	+	20580.7i	42781.2	−	74099.2i
7.3	−16.3218	−	28.2702i	−65.4143	−	113.301i	−276.801	+	479.434i	−805.880	−	1395.83i	−2135.35	+	3698.54i	−7030.62			1358.05			1283.45	−	2223.00i	−26306.8	+	45564.7i
7.4	−12.6406	−	21.8941i	88.4986	+	153.284i	−63.5673	+	110.102i	498.878	+	864.082i	2237.34	−	3875.19i	−9657.65			−9729.83			−5822.52	+	10084.9i	12612.2	−	21845.0i
7.5	−6.82378	−	11.8191i	−35.4198	−	61.3488i	162.872	−	282.103i	−572.036	−	990.795i	−483.393	+	837.262i	5106.36			−11433.2			7332.38	−	12700.1i	−7806.89	+	13521.9i
7.6	−3.83779	−	6.64725i	111.749	+	193.554i	226.543	−	392.383i	−746.119	−	1292.32i	857.737	−	1485.64i	8355.84			−7407.60			−15134.0	+	26212.9i	−5726.90	+	9919.28i
7.7	−3.46328	−	5.99858i	−8.56249	−	14.8307i	232.011	−	401.855i	781.382	+	1353.39i	−59.3086	+	102.726i	−83.0972			−6760.48			9694.87	−	16792.0i	5412.29	−	9374.37i
7.8	3.32582	+	5.76048i	−131.258	−	227.345i	233.878	−	405.088i	−77.5423	−	134.307i	873.077	−	1512.21i	−3034.24			6516.98			−24615.6	+	42635.4i	515.783	−	893.362i
7.9	7.35932	+	12.7467i	42.7370	+	74.0227i	147.681	−	255.791i	−1107.26	−	1917.83i	−629.031	+	1089.51i	−12185.9			11883.3			6188.59	−	10719.0i	16297.3	−	28227.8i
7.10	9.20750	+	15.9479i	85.3852	+	147.891i	86.4437	−	149.725i	795.817	+	1378.40i	−1572.37	+	2723.42i	2900.36			12612.2			−4739.75	+	8209.49i	−14655.0	+	25383.2i
7.11	10.9691	+	18.9991i	−35.9517	−	62.2702i	15.3560	−	26.5973i	242.418	+	419.881i	788.718	−	1366.10i	1688.25			11906.2			7256.45	−	12568.5i	−5318.24	+	9211.46i
7.12	17.0782	+	29.5803i	−62.2446	−	107.811i	−327.330	+	566.952i	−952.067	−	1649.03i	2126.05	−	3682.43i	11028.1			−4872.73			2092.73	−	3624.71i	32519.2	−	56324.9i
7.13	19.4836	+	33.7465i	89.2835	+	154.644i	−503.218	+	871.599i	−249.322	−	431.838i	−3479.12	+	6026.01i	698.529			−19266.8			−6101.58	+	10568.2i	9715.34	−	16827.5i
7.14	20.1948	+	34.9785i	−65.0904	−	112.740i	−559.662	+	969.363i	886.813	+	1536.00i	2628.98	−	4553.53i	−9612.95			−24529.6			1367.97	−	2369.40i	−35818.1	+	62038.7i
11.1	−19.9646	+	34.5797i	53.5081	−	92.6787i	−541.171	−	937.336i	−90.9465	+	157.524i	2136.54	+	3700.59i	6421.38			22773.3			4115.27	+	7127.85i	−3631.42	−	6289.81i
11.2	−17.0666	+	29.5602i	−104.220	+	180.515i	−326.535	−	565.575i	1253.36	−	2170.89i	−3557.37	−	6161.54i	4067.64			4815.16			−11882.3	−	20580.7i	42781.2	+	74099.2i
11.3	−16.3218	+	28.2702i	−65.4143	+	113.301i	−276.801	−	479.434i	−805.880	+	1395.83i	−2135.35	−	3698.54i	−7030.62			1358.05			1283.45	+	2223.00i	−26306.8	−	45564.7i
11.4	−12.6406	+	21.8941i	88.4986	−	153.284i	−63.5673	−	110.102i	498.878	−	864.082i	2237.34	+	3875.19i	−9657.65			−9729.83			−5822.52	−	10084.9i	12612.2	+	21845.0i
11.5	−6.82378	+	11.8191i	−35.4198	+	61.3488i	162.872	+	282.103i	−572.036	+	990.795i	−483.393	−	837.262i	5106.36			−11433.2			7332.38	+	12700.1i	−7806.89	−	13521.9i
11.6	−3.83779	+	6.64725i	111.749	−	193.554i	226.543	+	392.383i	−746.119	+	1292.32i	857.737	+	1485.64i	8355.84			−7407.60			−15134.0	−	26212.9i	−5726.90	−	9919.28i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	19.10.c.a	✓	28
19.c	even	3	1	inner	19.10.c.a	✓	28
19.c	even	3	1		361.10.a.e		14
19.d	odd	6	1		361.10.a.f		14

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
19.10.c.a	✓	28	1.a	even	1	1	trivial
19.10.c.a	✓	28	19.c	even	3	1	inner
361.10.a.e		14	19.c	even	3	1
361.10.a.f		14	19.d	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(19, [\chi])\).