Newform orbit 19.12.e.a

• Label: 19.12.e.a
• Level: $19$
• Weight: $12$
• Character orbit: 19.e
• Analytic conductor: $14.599$
• Analytic rank: $0$
• Dimension: $102$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.5985204306\)
Analytic rank:	\(0\)
Dimension:	\(102\)
Relative dimension:	\(17\) over \(\Q(\zeta_{9})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 102 q - 6 q^{2} - 795 q^{3} + 5928 q^{4} - 6 q^{5} - 14628 q^{6} - 57552 q^{7} - 294915 q^{8} + 466293 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−80.9691	−	29.4703i	−33.4486	−	189.696i	4118.63	+	3455.94i	−3179.74	+	2668.12i	−2882.11	+	16345.3i	10267.8	−	17784.4i	−143400.	−	248377.i	131598.	−	47897.7i	336091.	−	122327.i
4.2	−69.9954	−	25.4762i	99.0065	+	561.494i	2681.45	+	2250.01i	5923.01	−	4969.99i	7374.75	−	41824.3i	−7754.88	+	13431.8i	−54092.5	−	93690.9i	−139009.	+	50595.3i	−541200.	+	196981.i
4.3	−60.2192	−	21.9180i	−99.4009	−	563.731i	1577.09	+	1323.34i	6533.82	−	5482.52i	−6370.00	+	36126.1i	−22408.6	+	38812.9i	−344.434	−	596.577i	−141448.	+	51482.9i	−513627.	+	186945.i
4.4	−54.4681	−	19.8248i	80.4524	+	456.269i	1004.89	+	843.204i	−9812.84	+	8233.95i	4663.32	−	26447.0i	−32035.0	+	55486.3i	21336.7	+	36956.2i	−35244.6	+	12828.0i	697722.	−	253950.i
4.5	−50.9443	−	18.5422i	−22.1754	−	125.763i	682.648	+	572.810i	−808.961	+	678.799i	−1202.21	+	6818.08i	24300.7	−	42090.1i	31359.0	+	54315.4i	151139.	−	55010.2i	53798.3	−	19581.0i
4.6	−32.3045	−	11.7579i	−116.495	−	660.678i	−663.527	−	556.765i	−7687.95	+	6450.95i	−4004.84	+	22712.6i	−8232.79	+	14259.6i	50091.3	+	86760.7i	−256460.	+	93343.9i	324205.	−	118001.i
4.7	−29.5879	−	10.7691i	101.228	+	574.095i	−809.390	−	679.159i	294.009	−	246.703i	3187.36	−	18076.4i	35415.7	−	61341.8i	48876.6	+	84656.8i	−152875.	+	55641.8i	−11355.9	+	4133.20i
4.8	−20.6537	−	7.51732i	20.4380	+	115.910i	−1198.80	−	1005.91i	7249.02	−	6082.65i	449.211	−	2547.60i	−21184.0	+	36691.7i	39704.5	+	68770.1i	153446.	−	55849.9i	−195444.	+	71135.9i
4.9	1.95938	+	0.713155i	−2.20502	−	12.5053i	−1565.53	−	1313.63i	−2476.24	+	2077.81i	4.59775	−	26.0751i	−11314.9	+	19597.9i	−4265.80	−	7388.59i	166312.	−	60532.7i	−6333.69	+	2305.28i
4.10	7.94252	+	2.89084i	−109.852	−	623.002i	−1514.13	−	1270.51i	4857.62	−	4076.03i	928.497	−	5265.77i	29208.3	−	50590.3i	−17008.3	−	29459.2i	−209600.	+	76288.1i	50364.9	−	18331.3i
4.11	20.4195	+	7.43209i	126.620	+	718.097i	−1207.14	−	1012.91i	−1238.94	+	1039.59i	−2751.45	+	15604.2i	−12878.2	+	22305.7i	−39372.6	−	68195.4i	−333166.	+	121263.i	−33024.9	+	12020.1i
4.12	39.6813	+	14.4428i	16.2810	+	92.3342i	−202.848	−	170.209i	−9466.38	+	7943.23i	−687.514	+	3899.09i	37301.0	−	64607.3i	−48832.4	−	84580.2i	158203.	−	57581.3i	−490361.	+	178477.i
4.13	45.8399	+	16.6844i	58.4541	+	331.510i	254.070	+	213.190i	9215.11	−	7732.40i	−2851.50	+	16171.6i	20247.3	−	35069.4i	−41863.0	−	72508.8i	59981.8	−	21831.6i	551430.	−	200704.i
4.14	46.6591	+	16.9825i	−96.6035	−	547.865i	319.809	+	268.352i	−4521.96	+	3794.37i	4796.71	−	27203.5i	−26437.0	+	45790.2i	−40480.6	−	70114.4i	−124361.	+	45263.6i	−275429.	+	100248.i
4.15	52.8883	+	19.2498i	−53.5905	−	303.927i	857.760	+	719.746i	4925.70	−	4133.15i	3016.21	−	17105.8i	−17311.6	+	29984.6i	−26122.8	−	45246.0i	76964.0	−	28012.6i	340074.	−	123777.i
4.16	71.7173	+	26.1030i	72.8070	+	412.909i	2893.15	+	2427.64i	−1734.06	+	1455.05i	−5556.62	+	31513.2i	−12225.0	+	21174.2i	65968.6	+	114261.i	1270.93	−	462.581i	−162343.	+	59088.2i
4.17	80.1985	+	29.1899i	−85.2105	−	483.253i	4010.89	+	3365.53i	−11.2603	+	9.44853i	7272.33	−	41243.4i	28171.8	−	48795.0i	136034.	+	235617.i	−59808.7	+	21768.6i	−1178.86	+	429.071i
5.1	−80.9691	+	29.4703i	−33.4486	+	189.696i	4118.63	−	3455.94i	−3179.74	−	2668.12i	−2882.11	−	16345.3i	10267.8	+	17784.4i	−143400.	+	248377.i	131598.	+	47897.7i	336091.	+	122327.i
5.2	−69.9954	+	25.4762i	99.0065	−	561.494i	2681.45	−	2250.01i	5923.01	+	4969.99i	7374.75	+	41824.3i	−7754.88	−	13431.8i	−54092.5	+	93690.9i	−139009.	−	50595.3i	−541200.	−	196981.i
5.3	−60.2192	+	21.9180i	−99.4009	+	563.731i	1577.09	−	1323.34i	6533.82	+	5482.52i	−6370.00	−	36126.1i	−22408.6	−	38812.9i	−344.434	+	596.577i	−141448.	−	51482.9i	−513627.	−	186945.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.e	even	9	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	19.12.e.a	✓	102
19.e	even	9	1	inner	19.12.e.a	✓	102

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
19.12.e.a	✓	102	1.a	even	1	1	trivial
19.12.e.a	✓	102	19.e	even	9	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{12}^{\mathrm{new}}(19, [\chi])\).