Newform orbit 66.5.g.a

• Label: 66.5.g.a
• Level: $66$
• Weight: $5$
• Character orbit: 66.g
• Analytic conductor: $6.822$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	66.g (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82241756353\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 2 q^{3} + 128 q^{4} + 48 q^{6} + 80 q^{7} - 190 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−2.68999	+	0.874032i	−8.90700	−	1.29048i	6.47214	−	4.70228i	27.9092	+	9.06823i	25.0877	−	4.31361i	−43.3408	+	31.4889i	−13.3001	+	18.3060i	77.6693	+	22.9887i	−83.0014
5.2	−2.68999	+	0.874032i	−8.82215	+	1.78038i	6.47214	−	4.70228i	−33.5850	−	10.9124i	22.1754	−	12.5001i	12.6955	−	9.22385i	−13.3001	+	18.3060i	74.6605	−	31.4136i	99.8813
5.3	−2.68999	+	0.874032i	−4.09779	+	8.01300i	6.47214	−	4.70228i	32.9524	+	10.7069i	4.01941	−	25.1365i	32.4099	−	23.5472i	−13.3001	+	18.3060i	−47.4163	−	65.6711i	−97.9999
5.4	−2.68999	+	0.874032i	−0.424186	−	8.99000i	6.47214	−	4.70228i	−2.76348	−	0.897909i	8.99860	+	23.8123i	49.0021	−	35.6021i	−13.3001	+	18.3060i	−80.6401	+	7.62686i	8.21855
5.5	−2.68999	+	0.874032i	1.21864	+	8.91711i	6.47214	−	4.70228i	−21.1441	−	6.87012i	−11.0720	−	22.9218i	−18.4657	+	13.4161i	−13.3001	+	18.3060i	−78.0298	+	21.7336i	62.8821
5.6	−2.68999	+	0.874032i	6.34144	−	6.38640i	6.47214	−	4.70228i	33.2957	+	10.8184i	−11.4765	+	22.7220i	−23.8354	+	17.3174i	−13.3001	+	18.3060i	−0.572188	−	80.9980i	−99.0210
5.7	−2.68999	+	0.874032i	8.04754	+	4.02953i	6.47214	−	4.70228i	4.51606	+	1.46736i	−25.1698	−	3.80559i	55.7186	−	40.4820i	−13.3001	+	18.3060i	48.5258	+	64.8556i	−13.4307
5.8	−2.68999	+	0.874032i	8.66109	−	2.44654i	6.47214	−	4.70228i	−32.4758	−	10.5520i	−21.1599	+	14.1512i	−54.1844	+	39.3673i	−13.3001	+	18.3060i	69.0289	−	42.3794i	96.5825
5.9	2.68999	−	0.874032i	−8.68108	+	2.37464i	6.47214	−	4.70228i	2.76348	+	0.897909i	−21.2765	+	13.9753i	49.0021	−	35.6021i	13.3001	−	18.3060i	69.7222	−	41.2288i	8.21855
5.10	2.68999	−	0.874032i	−4.11421	+	8.00458i	6.47214	−	4.70228i	−33.2957	−	10.8184i	−4.07095	+	25.1282i	−23.8354	+	17.3174i	13.3001	−	18.3060i	−47.1465	−	65.8651i	−99.0210
5.11	2.68999	−	0.874032i	−3.97974	−	8.07228i	6.47214	−	4.70228i	−27.9092	−	9.06823i	−17.7609	−	18.2360i	−43.3408	+	31.4889i	13.3001	−	18.3060i	−49.3234	+	64.2511i	−83.0014
5.12	2.68999	−	0.874032i	−1.03295	−	8.94053i	6.47214	−	4.70228i	33.5850	+	10.9124i	−10.5929	−	23.1471i	12.6955	−	9.22385i	13.3001	−	18.3060i	−78.8660	+	18.4702i	99.8813
5.13	2.68999	−	0.874032i	0.349627	+	8.99321i	6.47214	−	4.70228i	32.4758	+	10.5520i	8.80084	+	23.8861i	−54.1844	+	39.3673i	13.3001	−	18.3060i	−80.7555	+	6.28853i	96.5825
5.14	2.68999	−	0.874032i	6.31913	+	6.40847i	6.47214	−	4.70228i	−4.51606	−	1.46736i	22.5996	+	11.7156i	55.7186	−	40.4820i	13.3001	−	18.3060i	−1.13710	+	80.9920i	−13.4307
5.15	2.68999	−	0.874032i	6.35453	−	6.37338i	6.47214	−	4.70228i	−32.9524	−	10.7069i	11.5231	−	22.6984i	32.4099	−	23.5472i	13.3001	−	18.3060i	−0.239961	−	80.9996i	−97.9999
5.16	2.68999	−	0.874032i	8.85726	−	1.59654i	6.47214	−	4.70228i	21.1441	+	6.87012i	22.4306	−	12.0362i	−18.4657	+	13.4161i	13.3001	−	18.3060i	75.9021	−	28.2819i	62.8821
47.1	−1.66251	−	2.28825i	−7.89796	+	4.31534i	−2.47214	+	7.60845i	9.70875	−	13.3630i	23.0050	+	10.8982i	−19.3710	+	59.6178i	21.5200	−	6.99226i	43.7556	−	68.1648i	−46.7186
47.2	−1.66251	−	2.28825i	−6.85719	−	5.82915i	−2.47214	+	7.60845i	−11.8680	+	16.3349i	−1.93840	+	25.3819i	4.86170	−	14.9628i	21.5200	−	6.99226i	13.0420	+	79.9431i	57.1090
47.3	−1.66251	−	2.28825i	−5.82791	+	6.85824i	−2.47214	+	7.60845i	−24.8627	+	34.2205i	25.3823	+	1.93380i	24.4331	−	75.1973i	21.5200	−	6.99226i	−13.0710	−	79.9384i	119.639
47.4	−1.66251	−	2.28825i	−4.72648	−	7.65901i	−2.47214	+	7.60845i	26.9487	−	37.0917i	−9.66788	+	23.5485i	9.48796	−	29.2009i	21.5200	−	6.99226i	−36.3208	+	72.4003i	−129.677

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
11.c	even	5	1	inner
33.h	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	66.5.g.a	✓	64
3.b	odd	2	1	inner	66.5.g.a	✓	64
11.c	even	5	1	inner	66.5.g.a	✓	64
33.h	odd	10	1	inner	66.5.g.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
66.5.g.a	✓	64	1.a	even	1	1	trivial
66.5.g.a	✓	64	3.b	odd	2	1	inner
66.5.g.a	✓	64	11.c	even	5	1	inner
66.5.g.a	✓	64	33.h	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(66, [\chi])\).