Newform orbit 63.6.o.a

• Label: 63.6.o.a
• Level: $63$
• Weight: $6$
• Character orbit: 63.o
• Analytic conductor: $10.104$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.1041806482\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 6 q^{2} + 574 q^{4} - 30 q^{7} + 156 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
20.1	−9.18933	−	5.30546i	−14.8309	+	4.80033i	40.2959	+	69.7945i	32.1784	+	55.7346i	161.754	+	34.5732i	−128.300	+	18.6049i		−	515.603i	196.914	−	142.387i		−	682.885i
20.2	−9.18933	−	5.30546i	14.8309	−	4.80033i	40.2959	+	69.7945i	−32.1784	−	55.7346i	−161.754	−	34.5732i	48.0376	+	120.413i		−	515.603i	196.914	−	142.387i			682.885i
20.3	−8.40544	−	4.85288i	−6.76084	+	14.0460i	31.1009	+	53.8683i	−32.8857	−	56.9596i	124.992	−	85.2535i	113.770	−	62.1566i		−	293.131i	−151.582	−	189.926i			638.361i
20.4	−8.40544	−	4.85288i	6.76084	−	14.0460i	31.1009	+	53.8683i	32.8857	+	56.9596i	−124.992	+	85.2535i	−3.05564	−	129.606i		−	293.131i	−151.582	−	189.926i		−	638.361i
20.5	−8.10965	−	4.68211i	−9.16477	−	12.6098i	27.8443	+	48.2277i	−41.6759	−	72.1848i	15.2827	+	145.171i	−128.575	+	16.6010i		−	221.824i	−75.0139	+	231.132i			780.524i
20.6	−8.10965	−	4.68211i	9.16477	+	12.6098i	27.8443	+	48.2277i	41.6759	+	72.1848i	−15.2827	−	145.171i	49.9104	+	119.649i		−	221.824i	−75.0139	+	231.132i		−	780.524i
20.7	−6.90679	−	3.98764i	−13.5113	−	7.77467i	15.8025	+	27.3707i	0.726757	+	1.25878i	62.3170	+	107.576i	119.993	−	49.0780i			3.15069i	122.109	+	210.091i		−	11.5922i
20.8	−6.90679	−	3.98764i	13.5113	+	7.77467i	15.8025	+	27.3707i	−0.726757	−	1.25878i	−62.3170	−	107.576i	−17.4938	−	128.456i			3.15069i	122.109	+	210.091i			11.5922i
20.9	−5.56054	−	3.21038i	−2.07465	+	15.4498i	4.61309	+	7.99011i	−9.29267	−	16.0954i	61.1359	−	79.2488i	−120.355	+	48.1831i			146.225i	−234.392	−	64.1057i			119.332i
20.10	−5.56054	−	3.21038i	2.07465	−	15.4498i	4.61309	+	7.99011i	9.29267	+	16.0954i	−61.1359	+	79.2488i	18.4499	+	128.322i			146.225i	−234.392	−	64.1057i		−	119.332i
20.11	−4.66729	−	2.69466i	−15.1594	+	3.63216i	−1.47762	−	2.55931i	13.2780	+	22.9982i	80.5407	+	23.8971i	58.2095	+	115.839i			188.385i	216.615	−	110.123i		−	143.119i
20.12	−4.66729	−	2.69466i	15.1594	−	3.63216i	−1.47762	−	2.55931i	−13.2780	−	22.9982i	−80.5407	−	23.8971i	−129.424	+	7.50861i			188.385i	216.615	−	110.123i			143.119i
20.13	−2.93016	−	1.69173i	−3.58345	+	15.1710i	−10.2761	−	17.7988i	47.2965	+	81.9200i	36.1652	−	38.3911i	59.9583	−	114.943i			177.808i	−217.318	−	108.729i		−	320.051i
20.14	−2.93016	−	1.69173i	3.58345	−	15.1710i	−10.2761	−	17.7988i	−47.2965	−	81.9200i	−36.1652	+	38.3911i	69.5648	−	109.397i			177.808i	−217.318	−	108.729i			320.051i
20.15	−2.69116	−	1.55374i	−10.2344	−	11.7583i	−11.1718	−	19.3501i	48.7868	+	84.5013i	9.27294	+	47.5451i	−124.613	−	35.7563i			168.872i	−33.5157	+	240.678i		−	303.209i
20.16	−2.69116	−	1.55374i	10.2344	+	11.7583i	−11.1718	−	19.3501i	−48.7868	−	84.5013i	−9.27294	−	47.5451i	93.2725	+	90.0402i			168.872i	−33.5157	+	240.678i			303.209i
20.17	−2.26766	−	1.30923i	−15.1407	+	3.70948i	−12.5718	−	21.7750i	−26.1836	−	45.3513i	39.1904	+	11.4108i	−66.1554	−	111.492i			149.629i	215.479	−	112.328i			137.122i
20.18	−2.26766	−	1.30923i	15.1407	−	3.70948i	−12.5718	−	21.7750i	26.1836	+	45.3513i	−39.1904	−	11.4108i	129.633	+	1.54629i			149.629i	215.479	−	112.328i		−	137.122i
20.19	0.868434	+	0.501391i	−8.37086	+	13.1502i	−15.4972	−	26.8420i	−10.2165	−	17.6955i	−13.8630	+	7.22305i	101.350	+	80.8400i		−	63.1697i	−102.857	−	220.158i		−	20.4898i
20.20	0.868434	+	0.501391i	8.37086	−	13.1502i	−15.4972	−	26.8420i	10.2165	+	17.6955i	13.8630	−	7.22305i	−120.685	−	47.3520i		−	63.1697i	−102.857	−	220.158i			20.4898i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
9.d	odd	6	1	inner
63.o	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	63.6.o.a	✓	76
3.b	odd	2	1		189.6.o.a		76
7.b	odd	2	1	inner	63.6.o.a	✓	76
9.c	even	3	1		189.6.o.a		76
9.d	odd	6	1	inner	63.6.o.a	✓	76
21.c	even	2	1		189.6.o.a		76
63.l	odd	6	1		189.6.o.a		76
63.o	even	6	1	inner	63.6.o.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.6.o.a	✓	76	1.a	even	1	1	trivial
63.6.o.a	✓	76	7.b	odd	2	1	inner
63.6.o.a	✓	76	9.d	odd	6	1	inner
63.6.o.a	✓	76	63.o	even	6	1	inner
189.6.o.a		76	3.b	odd	2	1
189.6.o.a		76	9.c	even	3	1
189.6.o.a		76	21.c	even	2	1
189.6.o.a		76	63.l	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(63, [\chi])\).