Newform orbit 3120.2.k.i

• Label: 3120.2.k.i
• Level: $3120$
• Weight: $2$
• Character orbit: 3120.k
• Analytic conductor: $24.913$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3120.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(24.9133254306\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
911.1		0		−1.65069	−	0.524620i		0			−	1.00000i		0				0.653717i		0		2.44955	+	1.73197i		0
911.2		0		−1.65069	+	0.524620i		0				1.00000i		0			−	0.653717i		0		2.44955	−	1.73197i		0
911.3		0		−1.58614	−	0.695811i		0				1.00000i		0				4.55195i		0		2.03169	+	2.20731i		0
911.4		0		−1.58614	+	0.695811i		0			−	1.00000i		0			−	4.55195i		0		2.03169	−	2.20731i		0
911.5		0		−1.46498	−	0.924033i		0			−	1.00000i		0			−	4.05340i		0		1.29233	+	2.70738i		0
911.6		0		−1.46498	+	0.924033i		0				1.00000i		0				4.05340i		0		1.29233	−	2.70738i		0
911.7		0		−1.18884	−	1.25963i		0				1.00000i		0				3.40132i		0		−0.173330	+	2.99499i		0
911.8		0		−1.18884	+	1.25963i		0			−	1.00000i		0			−	3.40132i		0		−0.173330	−	2.99499i		0
911.9		0		−1.04980	−	1.37765i		0				1.00000i		0			−	4.45625i		0		−0.795830	+	2.89252i		0
911.10		0		−1.04980	+	1.37765i		0			−	1.00000i		0				4.45625i		0		−0.795830	−	2.89252i		0
911.11		0		−0.665636	−	1.59904i		0			−	1.00000i		0				0.573804i		0		−2.11386	+	2.12876i		0
911.12		0		−0.665636	+	1.59904i		0				1.00000i		0			−	0.573804i		0		−2.11386	−	2.12876i		0
911.13		0		−0.648469	−	1.60608i		0				1.00000i		0			−	3.10745i		0		−2.15898	+	2.08298i		0
911.14		0		−0.648469	+	1.60608i		0			−	1.00000i		0				3.10745i		0		−2.15898	−	2.08298i		0
911.15		0		−0.483955	−	1.66307i		0			−	1.00000i		0				0.0981651i		0		−2.53157	+	1.60970i		0
911.16		0		−0.483955	+	1.66307i		0				1.00000i		0			−	0.0981651i		0		−2.53157	−	1.60970i		0
911.17		0		0.483955	−	1.66307i		0				1.00000i		0				0.0981651i		0		−2.53157	−	1.60970i		0
911.18		0		0.483955	+	1.66307i		0			−	1.00000i		0			−	0.0981651i		0		−2.53157	+	1.60970i		0
911.19		0		0.648469	−	1.60608i		0			−	1.00000i		0			−	3.10745i		0		−2.15898	−	2.08298i		0
911.20		0		0.648469	+	1.60608i		0				1.00000i		0				3.10745i		0		−2.15898	+	2.08298i		0

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	3120.2.k.i	✓	32
3.b	odd	2	1	inner	3120.2.k.i	✓	32
4.b	odd	2	1	inner	3120.2.k.i	✓	32
12.b	even	2	1	inner	3120.2.k.i	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3120.2.k.i	✓	32	1.a	even	1	1	trivial
3120.2.k.i	✓	32	3.b	odd	2	1	inner
3120.2.k.i	✓	32	4.b	odd	2	1	inner
3120.2.k.i	✓	32	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3120, [\chi])\):

T7^16 + 79*T7^14 + 2460*T7^12 + 37864*T7^10 + 291888*T7^8 + 962800*T7^6 + 617792*T7^4 + 112128*T7^2 + 1024

T11^16 - 87*T11^14 + 2828*T11^12 - 44312*T11^10 + 358620*T11^8 - 1482140*T11^6 + 2831856*T11^4 - 1826624*T11^2 + 246016