Newform orbit 66.4.h.a

• Label: 66.4.h.a
• Level: $66$
• Weight: $4$
• Character orbit: 66.h
• Analytic conductor: $3.894$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	66.h (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.89412606038\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{2} - q^{3} - 24 q^{4} - 32 q^{6} - 48 q^{8} - 33 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	0.618034	+	1.90211i	−5.19368	+	0.160184i	−3.23607	+	2.35114i	−1.14202	−	0.371066i	−3.51456	−	9.77997i	−15.8100	−	21.7606i	−6.47214	−	4.70228i	26.9487	−	1.66389i		−	2.40159i
17.2	0.618034	+	1.90211i	−3.65732	−	3.69107i	−3.23607	+	2.35114i	9.32256	+	3.02908i	4.76049	−	9.23784i	18.1216	+	24.9422i	−6.47214	−	4.70228i	−0.248023	+	26.9989i			19.6046i
17.3	0.618034	+	1.90211i	−0.564852	+	5.16536i	−3.23607	+	2.35114i	−16.0767	−	5.22364i	−10.1742	+	2.11796i	4.34702	+	5.98315i	−6.47214	−	4.70228i	−26.3619	−	5.83533i		−	33.8081i
17.4	0.618034	+	1.90211i	−0.327163	−	5.18584i	−3.23607	+	2.35114i	−16.5254	−	5.36942i	9.66186	−	3.82733i	−4.86030	−	6.68962i	−6.47214	−	4.70228i	−26.7859	+	3.39323i		−	34.7516i
17.5	0.618034	+	1.90211i	0.532835	+	5.16876i	−3.23607	+	2.35114i	20.8040	+	6.75962i	−9.50226	+	4.20798i	−10.9481	−	15.0687i	−6.47214	−	4.70228i	−26.4322	+	5.50820i			43.7492i
17.6	0.618034	+	1.90211i	5.04706	+	1.23578i	−3.23607	+	2.35114i	0.263485	+	0.0856114i	0.768665	+	10.3638i	12.5039	+	17.2102i	−6.47214	−	4.70228i	23.9457	+	12.4741i			0.554088i
29.1	−1.61803	−	1.17557i	−4.99353	+	1.43690i	1.23607	+	3.80423i	−0.0960686	−	0.132227i	9.76888	+	3.54528i	10.0627	−	3.26957i	2.47214	−	7.60845i	22.8706	−	14.3504i			0.326883i
29.2	−1.61803	−	1.17557i	−2.78254	−	4.38834i	1.23607	+	3.80423i	−4.33767	−	5.97029i	−0.656560	+	10.3715i	−6.49850	+	2.11149i	2.47214	−	7.60845i	−11.5150	+	24.4214i			14.7594i
29.3	−1.61803	−	1.17557i	−0.265554	+	5.18936i	1.23607	+	3.80423i	−2.83713	−	3.90497i	6.53014	−	8.08439i	−16.7863	+	5.45421i	2.47214	−	7.60845i	−26.8590	−	2.75612i			9.65361i
29.4	−1.61803	−	1.17557i	1.48082	−	4.98068i	1.23607	+	3.80423i	11.3394	+	15.6073i	−8.25116	+	6.31810i	26.3937	−	8.57584i	2.47214	−	7.60845i	−22.6143	−	14.7510i		−	38.5834i
29.5	−1.61803	−	1.17557i	5.03639	+	1.27860i	1.23607	+	3.80423i	9.10721	+	12.5350i	−6.64596	−	7.98944i	−30.4774	+	9.90272i	2.47214	−	7.60845i	23.7304	+	12.8790i		−	30.9882i
29.6	−1.61803	−	1.17557i	5.18753	−	0.299207i	1.23607	+	3.80423i	−9.82162	−	13.5183i	−8.74534	−	5.61418i	13.9517	−	4.53319i	2.47214	−	7.60845i	26.8210	−	3.10429i			33.4191i
35.1	0.618034	−	1.90211i	−5.19368	−	0.160184i	−3.23607	−	2.35114i	−1.14202	+	0.371066i	−3.51456	+	9.77997i	−15.8100	+	21.7606i	−6.47214	+	4.70228i	26.9487	+	1.66389i			2.40159i
35.2	0.618034	−	1.90211i	−3.65732	+	3.69107i	−3.23607	−	2.35114i	9.32256	−	3.02908i	4.76049	+	9.23784i	18.1216	−	24.9422i	−6.47214	+	4.70228i	−0.248023	−	26.9989i		−	19.6046i
35.3	0.618034	−	1.90211i	−0.564852	−	5.16536i	−3.23607	−	2.35114i	−16.0767	+	5.22364i	−10.1742	−	2.11796i	4.34702	−	5.98315i	−6.47214	+	4.70228i	−26.3619	+	5.83533i			33.8081i
35.4	0.618034	−	1.90211i	−0.327163	+	5.18584i	−3.23607	−	2.35114i	−16.5254	+	5.36942i	9.66186	+	3.82733i	−4.86030	+	6.68962i	−6.47214	+	4.70228i	−26.7859	−	3.39323i			34.7516i
35.5	0.618034	−	1.90211i	0.532835	−	5.16876i	−3.23607	−	2.35114i	20.8040	−	6.75962i	−9.50226	−	4.20798i	−10.9481	+	15.0687i	−6.47214	+	4.70228i	−26.4322	−	5.50820i		−	43.7492i
35.6	0.618034	−	1.90211i	5.04706	−	1.23578i	−3.23607	−	2.35114i	0.263485	−	0.0856114i	0.768665	−	10.3638i	12.5039	−	17.2102i	−6.47214	+	4.70228i	23.9457	−	12.4741i		−	0.554088i
41.1	−1.61803	+	1.17557i	−4.99353	−	1.43690i	1.23607	−	3.80423i	−0.0960686	+	0.132227i	9.76888	−	3.54528i	10.0627	+	3.26957i	2.47214	+	7.60845i	22.8706	+	14.3504i		−	0.326883i
41.2	−1.61803	+	1.17557i	−2.78254	+	4.38834i	1.23607	−	3.80423i	−4.33767	+	5.97029i	−0.656560	−	10.3715i	−6.49850	−	2.11149i	2.47214	+	7.60845i	−11.5150	−	24.4214i		−	14.7594i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
33.f	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	66.4.h.a	✓	24
3.b	odd	2	1		66.4.h.b	yes	24
11.d	odd	10	1		66.4.h.b	yes	24
33.f	even	10	1	inner	66.4.h.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
66.4.h.a	✓	24	1.a	even	1	1	trivial
66.4.h.a	✓	24	33.f	even	10	1	inner
66.4.h.b	yes	24	3.b	odd	2	1
66.4.h.b	yes	24	11.d	odd	10	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 642*T5^22 + 3105*T5^21 + 254874*T5^20 - 1993410*T5^19 - 77540270*T5^18 + 819457875*T5^17 + 31121205279*T5^16 - 38770868490*T5^15 - 3792846479184*T5^14 + 57337428245430*T5^13 + 1032382308076258*T5^12 - 4065560549703000*T5^11 - 93062490972931404*T5^10 - 418124134554773820*T5^9 + 5103988872164227641*T5^8 + 45707301129868667580*T5^7 + 197389392467745711142*T5^6 + 265681023262383914325*T5^5 + 68714215458034899219*T5^4 - 59627531793826464210*T5^3 + 1064243539017583800*T5^2 + 812226561156436800*T5 + 371169571078239376