Properties

Label 24.6.a.c
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

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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

\(f(q)\) \(=\) \( q + 9q^{3} + 38q^{5} + 120q^{7} + 81q^{9} + O(q^{10}) \) \( q + 9q^{3} + 38q^{5} + 120q^{7} + 81q^{9} + 524q^{11} - 962q^{13} + 342q^{15} - 1358q^{17} - 2284q^{19} + 1080q^{21} + 2552q^{23} - 1681q^{25} + 729q^{27} + 3966q^{29} - 2992q^{31} + 4716q^{33} + 4560q^{35} + 13206q^{37} - 8658q^{39} - 15126q^{41} - 7316q^{43} + 3078q^{45} - 6960q^{47} - 2407q^{49} - 12222q^{51} - 17482q^{53} + 19912q^{55} - 20556q^{57} + 33884q^{59} + 39118q^{61} + 9720q^{63} - 36556q^{65} + 32996q^{67} + 22968q^{69} + 14248q^{71} - 35990q^{73} - 15129q^{75} + 62880q^{77} - 29888q^{79} + 6561q^{81} - 51884q^{83} - 51604q^{85} + 35694q^{87} + 30714q^{89} - 115440q^{91} - 26928q^{93} - 86792q^{95} - 48478q^{97} + 42444q^{99} + O(q^{100}) \)

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 38.0000 0 120.000 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.c 1
3.b odd 2 1 72.6.a.b 1
4.b odd 2 1 48.6.a.b 1
5.b even 2 1 600.6.a.a 1
5.c odd 4 2 600.6.f.h 2
8.b even 2 1 192.6.a.b 1
8.d odd 2 1 192.6.a.j 1
12.b even 2 1 144.6.a.d 1
16.e even 4 2 768.6.d.f 2
16.f odd 4 2 768.6.d.m 2
24.f even 2 1 576.6.a.ba 1
24.h odd 2 1 576.6.a.bb 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.6.a.c 1 1.a even 1 1 trivial
48.6.a.b 1 4.b odd 2 1
72.6.a.b 1 3.b odd 2 1
144.6.a.d 1 12.b even 2 1
192.6.a.b 1 8.b even 2 1
192.6.a.j 1 8.d odd 2 1
576.6.a.ba 1 24.f even 2 1
576.6.a.bb 1 24.h odd 2 1
600.6.a.a 1 5.b even 2 1
600.6.f.h 2 5.c odd 4 2
768.6.d.f 2 16.e even 4 2
768.6.d.m 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 \( T_{5} - 38 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 9 T \)
$5$ \( 1 - 38 T + 3125 T^{2} \)
$7$ \( 1 - 120 T + 16807 T^{2} \)
$11$ \( 1 - 524 T + 161051 T^{2} \)
$13$ \( 1 + 962 T + 371293 T^{2} \)
$17$ \( 1 + 1358 T + 1419857 T^{2} \)
$19$ \( 1 + 2284 T + 2476099 T^{2} \)
$23$ \( 1 - 2552 T + 6436343 T^{2} \)
$29$ \( 1 - 3966 T + 20511149 T^{2} \)
$31$ \( 1 + 2992 T + 28629151 T^{2} \)
$37$ \( 1 - 13206 T + 69343957 T^{2} \)
$41$ \( 1 + 15126 T + 115856201 T^{2} \)
$43$ \( 1 + 7316 T + 147008443 T^{2} \)
$47$ \( 1 + 6960 T + 229345007 T^{2} \)
$53$ \( 1 + 17482 T + 418195493 T^{2} \)
$59$ \( 1 - 33884 T + 714924299 T^{2} \)
$61$ \( 1 - 39118 T + 844596301 T^{2} \)
$67$ \( 1 - 32996 T + 1350125107 T^{2} \)
$71$ \( 1 - 14248 T + 1804229351 T^{2} \)
$73$ \( 1 + 35990 T + 2073071593 T^{2} \)
$79$ \( 1 + 29888 T + 3077056399 T^{2} \)
$83$ \( 1 + 51884 T + 3939040643 T^{2} \)
$89$ \( 1 - 30714 T + 5584059449 T^{2} \)
$97$ \( 1 + 48478 T + 8587340257 T^{2} \)
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