Newform orbit 7350.2.a.u

• Label: 7350.2.a.u
• Level: $7350$
• Weight: $2$
• Character orbit: 7350.a
• Self dual: yes
• Analytic conductor: $58.690$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(58.6900454856\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q - q^2 + q^3 + q^4 - q^6 - q^8 + q^9 - 5 * q^11 + q^12 + 5 * q^13 + q^16 + 4 * q^17 - q^18 - 7 * q^19 + 5 * q^22 - q^23 - q^24 - 5 * q^26 + q^27 - 2 * q^31 - q^32 - 5 * q^33 - 4 * q^34 + q^36 - q^37 + 7 * q^38 + 5 * q^39 + 5 * q^41 - 12 * q^43 - 5 * q^44 + q^46 + 11 * q^47 + q^48 + 4 * q^51 + 5 * q^52 + 9 * q^53 - q^54 - 7 * q^57 + 4 * q^59 + 4 * q^61 + 2 * q^62 + q^64 + 5 * q^66 + 12 * q^67 + 4 * q^68 - q^69 + 2 * q^71 - q^72 - 10 * q^73 + q^74 - 7 * q^76 - 5 * q^78 - 12 * q^79 + q^81 - 5 * q^82 + 12 * q^83 + 12 * q^86 + 5 * q^88 + 14 * q^89 - q^92 - 2 * q^93 - 11 * q^94 - q^96 + 8 * q^97 - 5 * q^99

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

0

−1.00000

1.00000

1.00000

0

−1.00000

0

−1.00000

1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(3\)	\( -1 \)
\(5\)	\( +1 \)
\(7\)	\( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	7350.2.a.u		1
5.b	even	2	1		1470.2.a.l		1
7.b	odd	2	1		7350.2.a.a		1
7.c	even	3	2		1050.2.i.p		2
15.d	odd	2	1		4410.2.a.j		1
35.c	odd	2	1		1470.2.a.o		1
35.i	odd	6	2		1470.2.i.e		2
35.j	even	6	2		210.2.i.b	✓	2
35.l	odd	12	4		1050.2.o.g		4
105.g	even	2	1		4410.2.a.u		1
105.o	odd	6	2		630.2.k.g		2
140.p	odd	6	2		1680.2.bg.d		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
210.2.i.b	✓	2	35.j	even	6	2
630.2.k.g		2	105.o	odd	6	2
1050.2.i.p		2	7.c	even	3	2
1050.2.o.g		4	35.l	odd	12	4
1470.2.a.l		1	5.b	even	2	1
1470.2.a.o		1	35.c	odd	2	1
1470.2.i.e		2	35.i	odd	6	2
1680.2.bg.d		2	140.p	odd	6	2
4410.2.a.j		1	15.d	odd	2	1
4410.2.a.u		1	105.g	even	2	1
7350.2.a.a		1	7.b	odd	2	1
7350.2.a.u		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7350))\):

\( T_{11} + 5 \)

\( T_{13} - 5 \)

\( T_{17} - 4 \)

\( T_{19} + 7 \)

\( T_{23} + 1 \)

\( T_{31} + 2 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 1 \)
$3$	\( T - 1 \)
$5$	\( T \)
$7$	\( T \)
$11$	\( T + 5 \)