Newform orbit 1332.2.c.b

• Label: 1332.2.c.b
• Level: $1332$
• Weight: $2$
• Character orbit: 1332.c
• Analytic conductor: $10.636$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1332.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.6360735492\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 4 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1259.1	−1.40527	−	0.158797i		0		1.94957	+	0.446306i		−	3.67984i		0				4.25339i	−2.66880	−	0.936767i		0		−0.584348	+	5.17116i
1259.2	−1.40527	+	0.158797i		0		1.94957	−	0.446306i			3.67984i		0			−	4.25339i	−2.66880	+	0.936767i		0		−0.584348	−	5.17116i
1259.3	−1.32383	−	0.497471i		0		1.50505	+	1.31713i		−	2.50491i		0			−	3.15559i	−1.33719	−	2.49237i		0		−1.24612	+	3.31608i
1259.4	−1.32383	+	0.497471i		0		1.50505	−	1.31713i			2.50491i		0				3.15559i	−1.33719	+	2.49237i		0		−1.24612	−	3.31608i
1259.5	−1.23332	−	0.692040i		0		1.04216	+	1.70702i			2.19565i		0				2.28086i	−0.103995	−	2.82651i		0		1.51947	−	2.70794i
1259.6	−1.23332	+	0.692040i		0		1.04216	−	1.70702i		−	2.19565i		0			−	2.28086i	−0.103995	+	2.82651i		0		1.51947	+	2.70794i
1259.7	−1.21212	−	0.728534i		0		0.938478	+	1.76614i		−	2.90744i		0				0.569178i	0.149145	−	2.82449i		0		−2.11816	+	3.52417i
1259.8	−1.21212	+	0.728534i		0		0.938478	−	1.76614i			2.90744i		0			−	0.569178i	0.149145	+	2.82449i		0		−2.11816	−	3.52417i
1259.9	−1.05162	−	0.945564i		0		0.211817	+	1.98875i		−	2.01512i		0				4.22629i	1.65774	−	2.29170i		0		−1.90543	+	2.11914i
1259.10	−1.05162	+	0.945564i		0		0.211817	−	1.98875i			2.01512i		0			−	4.22629i	1.65774	+	2.29170i		0		−1.90543	−	2.11914i
1259.11	−1.01342	−	0.986398i		0		0.0540382	+	1.99927i			2.80662i		0				2.52425i	1.91731	−	2.07940i		0		2.76844	−	2.84428i
1259.12	−1.01342	+	0.986398i		0		0.0540382	−	1.99927i		−	2.80662i		0			−	2.52425i	1.91731	+	2.07940i		0		2.76844	+	2.84428i
1259.13	−0.555302	−	1.30063i		0		−1.38328	+	1.44449i		−	1.22318i		0			−	4.59531i	2.64688	+	0.997009i		0		−1.59090	+	0.679234i
1259.14	−0.555302	+	1.30063i		0		−1.38328	−	1.44449i			1.22318i		0				4.59531i	2.64688	−	0.997009i		0		−1.59090	−	0.679234i
1259.15	−0.431480	−	1.34678i		0		−1.62765	+	1.16222i		−	0.0180575i		0			−	0.954316i	2.26756	+	1.69062i		0		−0.0243195	+	0.00779145i
1259.16	−0.431480	+	1.34678i		0		−1.62765	−	1.16222i			0.0180575i		0				0.954316i	2.26756	−	1.69062i		0		−0.0243195	−	0.00779145i
1259.17	−0.393588	−	1.35834i		0		−1.69018	+	1.06925i			3.07829i		0				2.48267i	2.11764	+	1.87499i		0		4.18136	−	1.21158i
1259.18	−0.393588	+	1.35834i		0		−1.69018	−	1.06925i		−	3.07829i		0			−	2.48267i	2.11764	−	1.87499i		0		4.18136	+	1.21158i
1259.19	0.393588	−	1.35834i		0		−1.69018	−	1.06925i			3.07829i		0			−	2.48267i	−2.11764	+	1.87499i		0		4.18136	+	1.21158i
1259.20	0.393588	+	1.35834i		0		−1.69018	+	1.06925i		−	3.07829i		0				2.48267i	−2.11764	−	1.87499i		0		4.18136	−	1.21158i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1332.2.c.b	✓	36
3.b	odd	2	1	inner	1332.2.c.b	✓	36
4.b	odd	2	1	inner	1332.2.c.b	✓	36
12.b	even	2	1	inner	1332.2.c.b	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1332.2.c.b	✓	36	1.a	even	1	1	trivial
1332.2.c.b	✓	36	3.b	odd	2	1	inner
1332.2.c.b	✓	36	4.b	odd	2	1	inner
1332.2.c.b	✓	36	12.b	even	2	1	inner