Properties

Label 120.2.a.b
Level $120$
Weight $2$
Character orbit 120.a
Self dual yes
Analytic conductor $0.958$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{5} + q^{9} + O(q^{10}) \) \( q + q^{3} + q^{5} + q^{9} - 4q^{11} + 6q^{13} + q^{15} - 6q^{17} - 4q^{19} + q^{25} + q^{27} - 2q^{29} - 8q^{31} - 4q^{33} - 2q^{37} + 6q^{39} - 6q^{41} + 12q^{43} + q^{45} + 8q^{47} - 7q^{49} - 6q^{51} + 6q^{53} - 4q^{55} - 4q^{57} + 12q^{59} + 14q^{61} + 6q^{65} + 4q^{67} + 8q^{71} - 6q^{73} + q^{75} - 8q^{79} + q^{81} - 12q^{83} - 6q^{85} - 2q^{87} + 10q^{89} - 8q^{93} - 4q^{95} + 2q^{97} - 4q^{99} + O(q^{100}) \)

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
0 1.00000 0 1.00000 0 0 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 120.2.a.b 1
3.b odd 2 1 360.2.a.b 1
4.b odd 2 1 240.2.a.c 1
5.b even 2 1 600.2.a.c 1
5.c odd 4 2 600.2.f.b 2
7.b odd 2 1 5880.2.a.a 1
8.b even 2 1 960.2.a.c 1
8.d odd 2 1 960.2.a.j 1
9.c even 3 2 3240.2.q.g 2
9.d odd 6 2 3240.2.q.q 2
12.b even 2 1 720.2.a.d 1
15.d odd 2 1 1800.2.a.n 1
15.e even 4 2 1800.2.f.j 2
16.e even 4 2 3840.2.k.o 2
16.f odd 4 2 3840.2.k.j 2
20.d odd 2 1 1200.2.a.o 1
20.e even 4 2 1200.2.f.g 2
24.f even 2 1 2880.2.a.bb 1
24.h odd 2 1 2880.2.a.x 1
40.e odd 2 1 4800.2.a.r 1
40.f even 2 1 4800.2.a.cd 1
40.i odd 4 2 4800.2.f.bc 2
40.k even 4 2 4800.2.f.i 2
60.h even 2 1 3600.2.a.t 1
60.l odd 4 2 3600.2.f.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
120.2.a.b 1 1.a even 1 1 trivial
240.2.a.c 1 4.b odd 2 1
360.2.a.b 1 3.b odd 2 1
600.2.a.c 1 5.b even 2 1
600.2.f.b 2 5.c odd 4 2
720.2.a.d 1 12.b even 2 1
960.2.a.c 1 8.b even 2 1
960.2.a.j 1 8.d odd 2 1
1200.2.a.o 1 20.d odd 2 1
1200.2.f.g 2 20.e even 4 2
1800.2.a.n 1 15.d odd 2 1
1800.2.f.j 2 15.e even 4 2
2880.2.a.x 1 24.h odd 2 1
2880.2.a.bb 1 24.f even 2 1
3240.2.q.g 2 9.c even 3 2
3240.2.q.q 2 9.d odd 6 2
3600.2.a.t 1 60.h even 2 1
3600.2.f.c 2 60.l odd 4 2
3840.2.k.j 2 16.f odd 4 2
3840.2.k.o 2 16.e even 4 2
4800.2.a.r 1 40.e odd 2 1
4800.2.a.cd 1 40.f even 2 1
4800.2.f.i 2 40.k even 4 2
4800.2.f.bc 2 40.i odd 4 2
5880.2.a.a 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(120))\).