Newform orbit 74.6.h.a

• Label: 74.6.h.a
• Level: $74$
• Weight: $6$
• Character orbit: 74.h
• Analytic conductor: $11.868$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.8684026662\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(16\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) \)

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	−2.57115	+	3.06418i	−20.5579	+	17.2501i	−2.77837	−	15.7569i	15.9101	−	43.7127i		−	107.346i	202.247	+	73.6118i	55.4256	+	32.0000i	82.8635	−	469.942i	93.0361	+	161.143i
3.2	−2.57115	+	3.06418i	−16.2007	+	13.5940i	−2.77837	−	15.7569i	0.866934	−	2.38188i		−	84.5942i	−134.390	−	48.9139i	55.4256	+	32.0000i	35.4695	−	201.158i	5.06949	+	8.78062i
3.3	−2.57115	+	3.06418i	−5.46669	+	4.58709i	−2.77837	−	15.7569i	−35.9379	+	98.7386i		−	28.5450i	74.9073	+	27.2640i	55.4256	+	32.0000i	−33.3533	+	189.156i	−210.151	−	363.992i
3.4	−2.57115	+	3.06418i	−4.69686	+	3.94113i	−2.77837	−	15.7569i	9.28305	−	25.5050i		−	24.5252i	77.8232	+	28.3253i	55.4256	+	32.0000i	−35.6686	+	202.286i	54.2837	+	94.0221i
3.5	−2.57115	+	3.06418i	2.39572	−	2.01025i	−2.77837	−	15.7569i	36.3778	−	99.9471i			12.5096i	−172.609	−	62.8245i	55.4256	+	32.0000i	−40.4981	+	229.676i	212.723	+	368.447i
3.6	−2.57115	+	3.06418i	7.21134	−	6.05104i	−2.77837	−	15.7569i	−5.26761	+	14.4726i			37.6550i	−11.7126	−	4.26304i	55.4256	+	32.0000i	−26.8081	+	152.036i	−30.8029	−	53.3522i
3.7	−2.57115	+	3.06418i	18.1172	−	15.2021i	−2.77837	−	15.7569i	15.7606	−	43.3020i			94.6013i	83.7120	+	30.4687i	55.4256	+	32.0000i	54.9315	−	311.532i	92.1620	+	159.629i
3.8	−2.57115	+	3.06418i	20.6376	−	17.3170i	−2.77837	−	15.7569i	−28.8625	+	79.2990i			107.762i	−209.650	−	76.3065i	55.4256	+	32.0000i	83.8350	−	475.452i	−168.776	−	292.329i
3.9	2.57115	−	3.06418i	−20.6482	+	17.3259i	−2.77837	−	15.7569i	−24.4685	+	67.2268i			107.817i	−39.0875	−	14.2267i	−55.4256	−	32.0000i	83.9648	−	476.188i	143.082	+	247.826i
3.10	2.57115	−	3.06418i	−16.4794	+	13.8279i	−2.77837	−	15.7569i	14.6671	−	40.2975i			86.0494i	36.2322	+	13.1874i	−55.4256	−	32.0000i	38.1647	−	216.443i	−85.7674	−	148.554i
3.11	2.57115	−	3.06418i	−9.90239	+	8.30909i	−2.77837	−	15.7569i	16.4126	−	45.0933i			51.7066i	−20.3554	−	7.40876i	−55.4256	−	32.0000i	−13.1802	+	74.7486i	−95.9745	−	166.233i
3.12	2.57115	−	3.06418i	1.03890	−	0.871742i	−2.77837	−	15.7569i	−11.0838	+	30.4525i		−	5.42476i	194.404	+	70.7571i	−55.4256	−	32.0000i	−41.8771	+	237.497i	64.8138	+	112.261i
3.13	2.57115	−	3.06418i	2.44498	−	2.05158i	−2.77837	−	15.7569i	−23.1154	+	63.5089i		−	12.7668i	−54.4150	−	19.8054i	−55.4256	−	32.0000i	−40.4276	+	229.276i	135.170	+	234.121i
3.14	2.57115	−	3.06418i	10.7924	−	9.05588i	−2.77837	−	15.7569i	17.1692	−	47.1719i		−	56.3538i	−205.267	−	74.7112i	−55.4256	−	32.0000i	−7.73005	+	43.8393i	−100.399	−	173.895i
3.15	2.57115	−	3.06418i	12.3631	−	10.3739i	−2.77837	−	15.7569i	33.5955	−	92.3028i		−	64.5555i	200.133	+	72.8426i	−55.4256	−	32.0000i	3.03242	−	17.1977i	−196.453	−	340.267i
3.16	2.57115	−	3.06418i	21.8303	−	18.3178i	−2.77837	−	15.7569i	−10.1389	+	27.8564i		−	113.990i	−22.2808	−	8.10956i	−55.4256	−	32.0000i	98.8244	−	560.461i	59.2884	+	102.690i
21.1	−1.36808	+	3.75877i	−23.0035	+	8.37259i	−12.2567	−	10.2846i	48.7297	+	8.59237i		−	97.9193i	23.7455	−	134.667i	55.4256	−	32.0000i	272.912	−	229.000i	−98.9629	+	171.409i
21.2	−1.36808	+	3.75877i	−17.4563	+	6.35356i	−12.2567	−	10.2846i	−104.064	−	18.3493i		−	74.3062i	19.0842	−	108.232i	55.4256	−	32.0000i	78.2045	−	65.6213i	211.339	−	366.050i
21.3	−1.36808	+	3.75877i	−10.7367	+	3.90785i	−12.2567	−	10.2846i	−56.2384	−	9.91636i		−	45.7031i	−23.1802	+	131.461i	55.4256	−	32.0000i	−86.1429	+	72.2825i	114.212	−	197.821i
21.4	−1.36808	+	3.75877i	−10.5624	+	3.84441i	−12.2567	−	10.2846i	53.2500	+	9.38941i		−	44.9612i	−24.0440	+	136.360i	55.4256	−	32.0000i	−89.3632	+	74.9846i	−108.143	+	187.309i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
37.h	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	74.6.h.a	✓	96
37.h	even	18	1	inner	74.6.h.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
74.6.h.a	✓	96	1.a	even	1	1	trivial
74.6.h.a	✓	96	37.h	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(74, [\chi])\).