Properties

Label 24.6.a.b
Level 24
Weight 6
Character orbit 24.a
Self dual yes
Analytic conductor 3.849
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.84921167551\)
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

\(f(q)\) \(=\) \( q - 9q^{3} + 94q^{5} + 144q^{7} + 81q^{9} + O(q^{10}) \) \( q - 9q^{3} + 94q^{5} + 144q^{7} + 81q^{9} - 380q^{11} + 814q^{13} - 846q^{15} - 862q^{17} - 1156q^{19} - 1296q^{21} - 488q^{23} + 5711q^{25} - 729q^{27} - 5466q^{29} + 9560q^{31} + 3420q^{33} + 13536q^{35} - 10506q^{37} - 7326q^{39} - 5190q^{41} - 17084q^{43} + 7614q^{45} + 3168q^{47} + 3929q^{49} + 7758q^{51} - 24770q^{53} - 35720q^{55} + 10404q^{57} + 17380q^{59} + 4366q^{61} + 11664q^{63} + 76516q^{65} - 5284q^{67} + 4392q^{69} + 8360q^{71} + 39466q^{73} - 51399q^{75} - 54720q^{77} + 42376q^{79} + 6561q^{81} - 61828q^{83} - 81028q^{85} + 49194q^{87} - 63078q^{89} + 117216q^{91} - 86040q^{93} - 108664q^{95} - 16318q^{97} - 30780q^{99} + O(q^{100}) \)

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 −9.00000 0 94.0000 0 144.000 0 81.0000 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 24.6.a.b 1
3.b odd 2 1 72.6.a.a 1
4.b odd 2 1 48.6.a.e 1
5.b even 2 1 600.6.a.d 1
5.c odd 4 2 600.6.f.b 2
8.b even 2 1 192.6.a.i 1
8.d odd 2 1 192.6.a.a 1
12.b even 2 1 144.6.a.b 1
16.e even 4 2 768.6.d.d 2
16.f odd 4 2 768.6.d.o 2
24.f even 2 1 576.6.a.bf 1
24.h odd 2 1 576.6.a.bg 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.6.a.b 1 1.a even 1 1 trivial
48.6.a.e 1 4.b odd 2 1
72.6.a.a 1 3.b odd 2 1
144.6.a.b 1 12.b even 2 1
192.6.a.a 1 8.d odd 2 1
192.6.a.i 1 8.b even 2 1
576.6.a.bf 1 24.f even 2 1
576.6.a.bg 1 24.h odd 2 1
600.6.a.d 1 5.b even 2 1
600.6.f.b 2 5.c odd 4 2
768.6.d.d 2 16.e even 4 2
768.6.d.o 2 16.f odd 4 2

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 94 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 + 9 T \)
$5$ \( 1 - 94 T + 3125 T^{2} \)
$7$ \( 1 - 144 T + 16807 T^{2} \)
$11$ \( 1 + 380 T + 161051 T^{2} \)
$13$ \( 1 - 814 T + 371293 T^{2} \)
$17$ \( 1 + 862 T + 1419857 T^{2} \)
$19$ \( 1 + 1156 T + 2476099 T^{2} \)
$23$ \( 1 + 488 T + 6436343 T^{2} \)
$29$ \( 1 + 5466 T + 20511149 T^{2} \)
$31$ \( 1 - 9560 T + 28629151 T^{2} \)
$37$ \( 1 + 10506 T + 69343957 T^{2} \)
$41$ \( 1 + 5190 T + 115856201 T^{2} \)
$43$ \( 1 + 17084 T + 147008443 T^{2} \)
$47$ \( 1 - 3168 T + 229345007 T^{2} \)
$53$ \( 1 + 24770 T + 418195493 T^{2} \)
$59$ \( 1 - 17380 T + 714924299 T^{2} \)
$61$ \( 1 - 4366 T + 844596301 T^{2} \)
$67$ \( 1 + 5284 T + 1350125107 T^{2} \)
$71$ \( 1 - 8360 T + 1804229351 T^{2} \)
$73$ \( 1 - 39466 T + 2073071593 T^{2} \)
$79$ \( 1 - 42376 T + 3077056399 T^{2} \)
$83$ \( 1 + 61828 T + 3939040643 T^{2} \)
$89$ \( 1 + 63078 T + 5584059449 T^{2} \)
$97$ \( 1 + 16318 T + 8587340257 T^{2} \)
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