Properties

Label 104.2.a.a
Level 104
Weight 2
Character orbit 104.a
Self dual yes
Analytic conductor 0.830
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 104.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.830444181021\)
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

\(f(q)\) \(=\) \( q + q^{3} - q^{5} + 5q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} - q^{5} + 5q^{7} - 2q^{9} - 2q^{11} - q^{13} - q^{15} - 3q^{17} - 2q^{19} + 5q^{21} + 4q^{23} - 4q^{25} - 5q^{27} - 6q^{29} - 4q^{31} - 2q^{33} - 5q^{35} + 11q^{37} - q^{39} + 8q^{41} - q^{43} + 2q^{45} + 9q^{47} + 18q^{49} - 3q^{51} - 12q^{53} + 2q^{55} - 2q^{57} + 6q^{59} - 10q^{63} + q^{65} + 6q^{67} + 4q^{69} + 7q^{71} - 2q^{73} - 4q^{75} - 10q^{77} + 12q^{79} + q^{81} - 16q^{83} + 3q^{85} - 6q^{87} - 10q^{89} - 5q^{91} - 4q^{93} + 2q^{95} - 10q^{97} + 4q^{99} + O(q^{100}) \)

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 5.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 104.2.a.a 1
3.b odd 2 1 936.2.a.f 1
4.b odd 2 1 208.2.a.b 1
5.b even 2 1 2600.2.a.e 1
5.c odd 4 2 2600.2.d.f 2
7.b odd 2 1 5096.2.a.c 1
8.b even 2 1 832.2.a.c 1
8.d odd 2 1 832.2.a.h 1
12.b even 2 1 1872.2.a.l 1
13.b even 2 1 1352.2.a.b 1
13.c even 3 2 1352.2.i.b 2
13.d odd 4 2 1352.2.f.b 2
13.e even 6 2 1352.2.i.c 2
13.f odd 12 4 1352.2.o.a 4
16.e even 4 2 3328.2.b.a 2
16.f odd 4 2 3328.2.b.t 2
20.d odd 2 1 5200.2.a.bb 1
24.f even 2 1 7488.2.a.u 1
24.h odd 2 1 7488.2.a.x 1
52.b odd 2 1 2704.2.a.d 1
52.f even 4 2 2704.2.f.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
104.2.a.a 1 1.a even 1 1 trivial
208.2.a.b 1 4.b odd 2 1
832.2.a.c 1 8.b even 2 1
832.2.a.h 1 8.d odd 2 1
936.2.a.f 1 3.b odd 2 1
1352.2.a.b 1 13.b even 2 1
1352.2.f.b 2 13.d odd 4 2
1352.2.i.b 2 13.c even 3 2
1352.2.i.c 2 13.e even 6 2
1352.2.o.a 4 13.f odd 12 4
1872.2.a.l 1 12.b even 2 1
2600.2.a.e 1 5.b even 2 1
2600.2.d.f 2 5.c odd 4 2
2704.2.a.d 1 52.b odd 2 1
2704.2.f.e 2 52.f even 4 2
3328.2.b.a 2 16.e even 4 2
3328.2.b.t 2 16.f odd 4 2
5096.2.a.c 1 7.b odd 2 1
5200.2.a.bb 1 20.d odd 2 1
7488.2.a.u 1 24.f even 2 1
7488.2.a.x 1 24.h odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(13\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(104))\).