Properties

Label 24.2.a.a
Level 24
Weight 2
Character orbit 24.a
Self dual yes
Analytic conductor 0.192
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.191640964851\)
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

\(f(q)\) \(=\) \( q - q^{3} - 2q^{5} + q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{13} + 2q^{15} + 2q^{17} - 4q^{19} - 8q^{23} - q^{25} - q^{27} + 6q^{29} + 8q^{31} - 4q^{33} + 6q^{37} + 2q^{39} - 6q^{41} + 4q^{43} - 2q^{45} - 7q^{49} - 2q^{51} - 2q^{53} - 8q^{55} + 4q^{57} + 4q^{59} - 2q^{61} + 4q^{65} - 4q^{67} + 8q^{69} + 8q^{71} + 10q^{73} + q^{75} - 8q^{79} + q^{81} - 4q^{83} - 4q^{85} - 6q^{87} - 6q^{89} - 8q^{93} + 8q^{95} + 2q^{97} + 4q^{99} + O(q^{100}) \)

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 −2.00000 0 0 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 24.2.a.a 1
3.b odd 2 1 72.2.a.a 1
4.b odd 2 1 48.2.a.a 1
5.b even 2 1 600.2.a.h 1
5.c odd 4 2 600.2.f.e 2
7.b odd 2 1 1176.2.a.i 1
7.c even 3 2 1176.2.q.i 2
7.d odd 6 2 1176.2.q.a 2
8.b even 2 1 192.2.a.d 1
8.d odd 2 1 192.2.a.b 1
9.c even 3 2 648.2.i.g 2
9.d odd 6 2 648.2.i.b 2
11.b odd 2 1 2904.2.a.c 1
12.b even 2 1 144.2.a.b 1
13.b even 2 1 4056.2.a.i 1
13.d odd 4 2 4056.2.c.e 2
15.d odd 2 1 1800.2.a.m 1
15.e even 4 2 1800.2.f.c 2
16.e even 4 2 768.2.d.e 2
16.f odd 4 2 768.2.d.d 2
17.b even 2 1 6936.2.a.p 1
19.b odd 2 1 8664.2.a.j 1
20.d odd 2 1 1200.2.a.d 1
20.e even 4 2 1200.2.f.b 2
21.c even 2 1 3528.2.a.d 1
21.g even 6 2 3528.2.s.y 2
21.h odd 6 2 3528.2.s.j 2
24.f even 2 1 576.2.a.b 1
24.h odd 2 1 576.2.a.d 1
28.d even 2 1 2352.2.a.i 1
28.f even 6 2 2352.2.q.r 2
28.g odd 6 2 2352.2.q.l 2
33.d even 2 1 8712.2.a.u 1
36.f odd 6 2 1296.2.i.m 2
36.h even 6 2 1296.2.i.e 2
40.e odd 2 1 4800.2.a.cc 1
40.f even 2 1 4800.2.a.q 1
40.i odd 4 2 4800.2.f.d 2
40.k even 4 2 4800.2.f.bg 2
44.c even 2 1 5808.2.a.s 1
48.i odd 4 2 2304.2.d.i 2
48.k even 4 2 2304.2.d.k 2
52.b odd 2 1 8112.2.a.be 1
56.e even 2 1 9408.2.a.cc 1
56.h odd 2 1 9408.2.a.h 1
60.h even 2 1 3600.2.a.v 1
60.l odd 4 2 3600.2.f.r 2
84.h odd 2 1 7056.2.a.q 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.2.a.a 1 1.a even 1 1 trivial
48.2.a.a 1 4.b odd 2 1
72.2.a.a 1 3.b odd 2 1
144.2.a.b 1 12.b even 2 1
192.2.a.b 1 8.d odd 2 1
192.2.a.d 1 8.b even 2 1
576.2.a.b 1 24.f even 2 1
576.2.a.d 1 24.h odd 2 1
600.2.a.h 1 5.b even 2 1
600.2.f.e 2 5.c odd 4 2
648.2.i.b 2 9.d odd 6 2
648.2.i.g 2 9.c even 3 2
768.2.d.d 2 16.f odd 4 2
768.2.d.e 2 16.e even 4 2
1176.2.a.i 1 7.b odd 2 1
1176.2.q.a 2 7.d odd 6 2
1176.2.q.i 2 7.c even 3 2
1200.2.a.d 1 20.d odd 2 1
1200.2.f.b 2 20.e even 4 2
1296.2.i.e 2 36.h even 6 2
1296.2.i.m 2 36.f odd 6 2
1800.2.a.m 1 15.d odd 2 1
1800.2.f.c 2 15.e even 4 2
2304.2.d.i 2 48.i odd 4 2
2304.2.d.k 2 48.k even 4 2
2352.2.a.i 1 28.d even 2 1
2352.2.q.l 2 28.g odd 6 2
2352.2.q.r 2 28.f even 6 2
2904.2.a.c 1 11.b odd 2 1
3528.2.a.d 1 21.c even 2 1
3528.2.s.j 2 21.h odd 6 2
3528.2.s.y 2 21.g even 6 2
3600.2.a.v 1 60.h even 2 1
3600.2.f.r 2 60.l odd 4 2
4056.2.a.i 1 13.b even 2 1
4056.2.c.e 2 13.d odd 4 2
4800.2.a.q 1 40.f even 2 1
4800.2.a.cc 1 40.e odd 2 1
4800.2.f.d 2 40.i odd 4 2
4800.2.f.bg 2 40.k even 4 2
5808.2.a.s 1 44.c even 2 1
6936.2.a.p 1 17.b even 2 1
7056.2.a.q 1 84.h odd 2 1
8112.2.a.be 1 52.b odd 2 1
8664.2.a.j 1 19.b odd 2 1
8712.2.a.u 1 33.d even 2 1
9408.2.a.h 1 56.h odd 2 1
9408.2.a.cc 1 56.e even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 + T \)
$5$ \( 1 + 2 T + 5 T^{2} \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( 1 - 4 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - 2 T + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 + 8 T + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 - 8 T + 31 T^{2} \)
$37$ \( 1 - 6 T + 37 T^{2} \)
$41$ \( 1 + 6 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 + 2 T + 53 T^{2} \)
$59$ \( 1 - 4 T + 59 T^{2} \)
$61$ \( 1 + 2 T + 61 T^{2} \)
$67$ \( 1 + 4 T + 67 T^{2} \)
$71$ \( 1 - 8 T + 71 T^{2} \)
$73$ \( 1 - 10 T + 73 T^{2} \)
$79$ \( 1 + 8 T + 79 T^{2} \)
$83$ \( 1 + 4 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 2 T + 97 T^{2} \)
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