Properties

Label 100.2.a.a
Level 100
Weight 2
Character orbit 100.a
Self dual yes
Analytic conductor 0.799
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 100.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.798504020213\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{3} - 2q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - 2q^{7} + q^{9} - 2q^{13} + 6q^{17} - 4q^{19} - 4q^{21} - 6q^{23} - 4q^{27} + 6q^{29} - 4q^{31} - 2q^{37} - 4q^{39} + 6q^{41} + 10q^{43} + 6q^{47} - 3q^{49} + 12q^{51} + 6q^{53} - 8q^{57} + 12q^{59} + 2q^{61} - 2q^{63} - 2q^{67} - 12q^{69} - 12q^{71} - 2q^{73} + 8q^{79} - 11q^{81} - 6q^{83} + 12q^{87} - 6q^{89} + 4q^{91} - 8q^{93} - 2q^{97} + O(q^{100}) \)

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 2.00000 0 0 0 −2.00000 0 1.00000 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 100.2.a.a 1
3.b odd 2 1 900.2.a.b 1
4.b odd 2 1 400.2.a.c 1
5.b even 2 1 20.2.a.a 1
5.c odd 4 2 100.2.c.a 2
7.b odd 2 1 4900.2.a.e 1
8.b even 2 1 1600.2.a.c 1
8.d odd 2 1 1600.2.a.w 1
12.b even 2 1 3600.2.a.be 1
15.d odd 2 1 180.2.a.a 1
15.e even 4 2 900.2.d.c 2
20.d odd 2 1 80.2.a.b 1
20.e even 4 2 400.2.c.b 2
35.c odd 2 1 980.2.a.h 1
35.f even 4 2 4900.2.e.f 2
35.i odd 6 2 980.2.i.c 2
35.j even 6 2 980.2.i.i 2
40.e odd 2 1 320.2.a.a 1
40.f even 2 1 320.2.a.f 1
40.i odd 4 2 1600.2.c.d 2
40.k even 4 2 1600.2.c.e 2
45.h odd 6 2 1620.2.i.b 2
45.j even 6 2 1620.2.i.h 2
55.d odd 2 1 2420.2.a.a 1
60.h even 2 1 720.2.a.h 1
60.l odd 4 2 3600.2.f.j 2
65.d even 2 1 3380.2.a.c 1
65.g odd 4 2 3380.2.f.b 2
80.k odd 4 2 1280.2.d.g 2
80.q even 4 2 1280.2.d.c 2
85.c even 2 1 5780.2.a.f 1
85.j even 4 2 5780.2.c.a 2
95.d odd 2 1 7220.2.a.f 1
105.g even 2 1 8820.2.a.g 1
120.i odd 2 1 2880.2.a.m 1
120.m even 2 1 2880.2.a.f 1
140.c even 2 1 3920.2.a.h 1
220.g even 2 1 9680.2.a.ba 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
20.2.a.a 1 5.b even 2 1
80.2.a.b 1 20.d odd 2 1
100.2.a.a 1 1.a even 1 1 trivial
100.2.c.a 2 5.c odd 4 2
180.2.a.a 1 15.d odd 2 1
320.2.a.a 1 40.e odd 2 1
320.2.a.f 1 40.f even 2 1
400.2.a.c 1 4.b odd 2 1
400.2.c.b 2 20.e even 4 2
720.2.a.h 1 60.h even 2 1
900.2.a.b 1 3.b odd 2 1
900.2.d.c 2 15.e even 4 2
980.2.a.h 1 35.c odd 2 1
980.2.i.c 2 35.i odd 6 2
980.2.i.i 2 35.j even 6 2
1280.2.d.c 2 80.q even 4 2
1280.2.d.g 2 80.k odd 4 2
1600.2.a.c 1 8.b even 2 1
1600.2.a.w 1 8.d odd 2 1
1600.2.c.d 2 40.i odd 4 2
1600.2.c.e 2 40.k even 4 2
1620.2.i.b 2 45.h odd 6 2
1620.2.i.h 2 45.j even 6 2
2420.2.a.a 1 55.d odd 2 1
2880.2.a.f 1 120.m even 2 1
2880.2.a.m 1 120.i odd 2 1
3380.2.a.c 1 65.d even 2 1
3380.2.f.b 2 65.g odd 4 2
3600.2.a.be 1 12.b even 2 1
3600.2.f.j 2 60.l odd 4 2
3920.2.a.h 1 140.c even 2 1
4900.2.a.e 1 7.b odd 2 1
4900.2.e.f 2 35.f even 4 2
5780.2.a.f 1 85.c even 2 1
5780.2.c.a 2 85.j even 4 2
7220.2.a.f 1 95.d odd 2 1
8820.2.a.g 1 105.g even 2 1
9680.2.a.ba 1 220.g even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(\Gamma_0(100))\).