Newform orbit 666.2.h.c

• Label: 666.2.h.c
• Level: $666$
• Weight: $2$
• Character orbit: 666.h
• Analytic conductor: $5.318$
• Analytic rank: $0$
• Dimension: $38$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.31803677462\)
Analytic rank:	\(0\)
Dimension:	\(38\)
Relative dimension:	\(19\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 38 q + 38 q^{2} - 2 q^{3} + 38 q^{4} - 4 q^{5} - 2 q^{6} + q^{7} + 38 q^{8} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
121.1	1.00000			−1.72390	+	0.167877i	1.00000			−3.70230			−1.72390	+	0.167877i	−0.330849	+	0.573047i	1.00000			2.94363	−	0.578805i	−3.70230
121.2	1.00000			−1.68864	+	0.385344i	1.00000			3.96916			−1.68864	+	0.385344i	1.05023	−	1.81906i	1.00000			2.70302	−	1.30142i	3.96916
121.3	1.00000			−1.61518	−	0.625457i	1.00000			2.52032			−1.61518	−	0.625457i	−1.45985	+	2.52854i	1.00000			2.21761	+	2.02045i	2.52032
121.4	1.00000			−1.34882	+	1.08659i	1.00000			−0.495406			−1.34882	+	1.08659i	−2.03036	+	3.51669i	1.00000			0.638625	−	2.93124i	−0.495406
121.5	1.00000			−1.12306	−	1.31861i	1.00000			0.457071			−1.12306	−	1.31861i	2.24881	−	3.89506i	1.00000			−0.477485	+	2.96176i	0.457071
121.6	1.00000			−1.09407	−	1.34276i	1.00000			−2.22000			−1.09407	−	1.34276i	−0.959017	+	1.66107i	1.00000			−0.606007	+	2.93816i	−2.22000
121.7	1.00000			−1.07244	+	1.36010i	1.00000			1.22505			−1.07244	+	1.36010i	1.29500	−	2.24301i	1.00000			−0.699738	−	2.91725i	1.22505
121.8	1.00000			−0.543399	+	1.64460i	1.00000			−3.51311			−0.543399	+	1.64460i	2.20815	−	3.82462i	1.00000			−2.40943	−	1.78735i	−3.51311
121.9	1.00000			−0.367479	−	1.69262i	1.00000			−2.43204			−0.367479	−	1.69262i	−0.0737984	+	0.127823i	1.00000			−2.72992	+	1.24400i	−2.43204
121.10	1.00000			−0.266458	−	1.71143i	1.00000			2.46736			−0.266458	−	1.71143i	−0.202832	+	0.351316i	1.00000			−2.85800	+	0.912048i	2.46736
121.11	1.00000			−0.124130	+	1.72760i	1.00000			1.34325			−0.124130	+	1.72760i	−0.00815087	+	0.0141177i	1.00000			−2.96918	−	0.428893i	1.34325
121.12	1.00000			0.600169	+	1.62475i	1.00000			−2.29481			0.600169	+	1.62475i	−1.88616	+	3.26692i	1.00000			−2.27960	+	1.95024i	−2.29481
121.13	1.00000			0.725216	−	1.57292i	1.00000			−1.02077			0.725216	−	1.57292i	0.251154	−	0.435011i	1.00000			−1.94812	−	2.28141i	−1.02077
121.14	1.00000			1.13949	+	1.30444i	1.00000			2.72110			1.13949	+	1.30444i	−0.0957449	+	0.165835i	1.00000			−0.403115	+	2.97279i	2.72110
121.15	1.00000			1.30864	−	1.13466i	1.00000			0.219776			1.30864	−	1.13466i	1.50224	−	2.60196i	1.00000			0.425075	−	2.96973i	0.219776
121.16	1.00000			1.34292	+	1.09388i	1.00000			−2.55391			1.34292	+	1.09388i	1.70038	−	2.94514i	1.00000			0.606853	+	2.93798i	−2.55391
121.17	1.00000			1.38847	−	1.03545i	1.00000			2.81288			1.38847	−	1.03545i	−1.72500	+	2.98779i	1.00000			0.855671	−	2.87538i	2.81288
121.18	1.00000			1.73083	+	0.0651450i	1.00000			0.204308			1.73083	+	0.0651450i	1.30647	−	2.26288i	1.00000			2.99151	+	0.225509i	0.204308
121.19	1.00000			1.73185	−	0.0264065i	1.00000			−1.70793			1.73185	−	0.0264065i	−2.29068	+	3.96757i	1.00000			2.99861	−	0.0914641i	−1.70793
655.1	1.00000			−1.72390	−	0.167877i	1.00000			−3.70230			−1.72390	−	0.167877i	−0.330849	−	0.573047i	1.00000			2.94363	+	0.578805i	−3.70230

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
333.h	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	666.2.h.c	yes	38
3.b	odd	2	1		1998.2.h.c		38
9.c	even	3	1		666.2.g.c	✓	38
9.d	odd	6	1		1998.2.g.c		38
37.c	even	3	1		666.2.g.c	✓	38
111.i	odd	6	1		1998.2.g.c		38
333.h	even	3	1	inner	666.2.h.c	yes	38
333.l	odd	6	1		1998.2.h.c		38

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
666.2.g.c	✓	38	9.c	even	3	1
666.2.g.c	✓	38	37.c	even	3	1
666.2.h.c	yes	38	1.a	even	1	1	trivial
666.2.h.c	yes	38	333.h	even	3	1	inner
1998.2.g.c		38	9.d	odd	6	1
1998.2.g.c		38	111.i	odd	6	1
1998.2.h.c		38	3.b	odd	2	1
1998.2.h.c		38	333.l	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^19 + 2*T5^18 - 48*T5^17 - 94*T5^16 + 928*T5^15 + 1755*T5^14 - 9417*T5^13 - 16953*T5^12 + 54426*T5^11 + 91069*T5^10 - 181438*T5^9 - 268872*T5^8 + 339041*T5^7 + 399814*T5^6 - 334500*T5^5 - 245406*T5^4 + 146547*T5^3 + 29520*T5^2 - 20736*T5 + 2268