Newform orbit 1332.2.q.a

• Label: 1332.2.q.a
• Level: $1332$
• Weight: $2$
• Character orbit: 1332.q
• Analytic conductor: $10.636$
• Analytic rank: $0$
• Dimension: $76$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1332.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.6360735492\)
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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 2 q^{3} + q^{7} + 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
529.1		0		−1.73155	−	0.0417057i		0			−	2.68045i		0		2.22374	+	3.85164i		0		2.99652	+	0.144431i		0
529.2		0		−1.73043	−	0.0750196i		0			−	2.47125i		0		0.161941	+	0.280489i		0		2.98874	+	0.259632i		0
529.3		0		−1.71651	−	0.231520i		0				2.34976i		0		−0.443318	−	0.767849i		0		2.89280	+	0.794813i		0
529.4		0		−1.69409	+	0.360659i		0				1.43349i		0		−1.08967	−	1.88736i		0		2.73985	−	1.22197i		0
529.5		0		−1.69226	+	0.369137i		0				2.43118i		0		2.24645	+	3.89097i		0		2.72748	−	1.24935i		0
529.6		0		−1.62704	−	0.593911i		0			−	3.08020i		0		−1.53987	−	2.66714i		0		2.29454	+	1.93264i		0
529.7		0		−1.48001	+	0.899767i		0			−	1.77579i		0		−2.60677	−	4.51506i		0		1.38084	−	2.66332i		0
529.8		0		−1.40279	+	1.01596i		0				3.31919i		0		1.10127	+	1.90746i		0		0.935659	−	2.85036i		0
529.9		0		−1.39506	−	1.02655i		0			−	0.771580i		0		0.896869	+	1.55342i		0		0.892409	+	2.86419i		0
529.10		0		−1.30436	−	1.13958i		0				3.35988i		0		−0.817317	−	1.41563i		0		0.402708	+	2.97285i		0
529.11		0		−1.14223	−	1.30204i		0				0.819633i		0		−1.35502	−	2.34697i		0		−0.390615	+	2.97446i		0
529.12		0		−1.07782	+	1.35584i		0			−	2.30361i		0		0.902939	+	1.56394i		0		−0.676624	−	2.92270i		0
529.13		0		−1.04460	+	1.38159i		0				0.318247i		0		0.590692	+	1.02311i		0		−0.817603	−	2.88644i		0
529.14		0		−0.789421	−	1.54169i		0			−	1.43521i		0		1.64322	+	2.84613i		0		−1.75363	+	2.43409i		0
529.15		0		−0.543876	+	1.64444i		0			−	0.131988i		0		−0.159646	−	0.276515i		0		−2.40840	−	1.78875i		0
529.16		0		−0.360651	−	1.69409i		0				3.50945i		0		1.75752	+	3.04412i		0		−2.73986	+	1.22195i		0
529.17		0		−0.308825	−	1.70430i		0			−	4.29028i		0		−0.631595	−	1.09395i		0		−2.80925	+	1.05266i		0
529.18		0		−0.284098	+	1.70859i		0			−	4.18773i		0		−1.65189	−	2.86116i		0		−2.83858	−	0.970816i		0
529.19		0		−0.178802	+	1.72280i		0				2.74917i		0		−0.106731	−	0.184863i		0		−2.93606	−	0.616080i		0
529.20		0		−0.125151	−	1.72752i		0			−	0.898134i		0		−1.28125	−	2.21918i		0		−2.96867	+	0.432404i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
333.k	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1332.2.q.a	✓	76
3.b	odd	2	1		3996.2.q.a		76
9.c	even	3	1		1332.2.bn.a	yes	76
9.d	odd	6	1		3996.2.bn.a		76
37.e	even	6	1		1332.2.bn.a	yes	76
111.h	odd	6	1		3996.2.bn.a		76
333.k	even	6	1	inner	1332.2.q.a	✓	76
333.v	odd	6	1		3996.2.q.a		76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1332.2.q.a	✓	76	1.a	even	1	1	trivial
1332.2.q.a	✓	76	333.k	even	6	1	inner
1332.2.bn.a	yes	76	9.c	even	3	1
1332.2.bn.a	yes	76	37.e	even	6	1
3996.2.q.a		76	3.b	odd	2	1
3996.2.q.a		76	333.v	odd	6	1
3996.2.bn.a		76	9.d	odd	6	1
3996.2.bn.a		76	111.h	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1332, [\chi])\).