Properties

Label 24.12.a.c
Level 24
Weight 12
Character orbit 24.a
Self dual yes
Analytic conductor 18.440
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.4402363334\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + 243q^{3} + 1870q^{5} - 72312q^{7} + 59049q^{9} + O(q^{10}) \) \( q + 243q^{3} + 1870q^{5} - 72312q^{7} + 59049q^{9} + 147940q^{11} - 1562858q^{13} + 454410q^{15} - 145774q^{17} + 1096796q^{19} - 17571816q^{21} - 60014264q^{23} - 45331225q^{25} + 14348907q^{27} - 19626954q^{29} - 239950480q^{31} + 35949420q^{33} - 135223440q^{35} + 488238078q^{37} - 379774494q^{39} + 47066010q^{41} + 428866948q^{43} + 110421630q^{45} + 450903216q^{47} + 3251698601q^{49} - 35423082q^{51} + 4336685950q^{53} + 276647800q^{55} + 266521428q^{57} - 8937556460q^{59} + 4673884486q^{61} - 4269951288q^{63} - 2922544460q^{65} + 7498937612q^{67} - 14583466152q^{69} - 27032101480q^{71} + 11676141658q^{73} - 11015487675q^{75} - 10697837280q^{77} + 2478876544q^{79} + 3486784401q^{81} + 42745596956q^{83} - 272597380q^{85} - 4769349822q^{87} - 93270772662q^{89} + 113013387696q^{91} - 58307966640q^{93} + 2051008520q^{95} + 118032786914q^{97} + 8735709060q^{99} + O(q^{100}) \)

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
0 243.000 0 1870.00 0 −72312.0 0 59049.0 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 24.12.a.c 1
3.b odd 2 1 72.12.a.a 1
4.b odd 2 1 48.12.a.b 1
8.b even 2 1 192.12.a.e 1
8.d odd 2 1 192.12.a.o 1
12.b even 2 1 144.12.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.12.a.c 1 1.a even 1 1 trivial
48.12.a.b 1 4.b odd 2 1
72.12.a.a 1 3.b odd 2 1
144.12.a.g 1 12.b even 2 1
192.12.a.e 1 8.b even 2 1
192.12.a.o 1 8.d odd 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 1870 \) acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(24))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 - 243 T \)
$5$ \( 1 - 1870 T + 48828125 T^{2} \)
$7$ \( 1 + 72312 T + 1977326743 T^{2} \)
$11$ \( 1 - 147940 T + 285311670611 T^{2} \)
$13$ \( 1 + 1562858 T + 1792160394037 T^{2} \)
$17$ \( 1 + 145774 T + 34271896307633 T^{2} \)
$19$ \( 1 - 1096796 T + 116490258898219 T^{2} \)
$23$ \( 1 + 60014264 T + 952809757913927 T^{2} \)
$29$ \( 1 + 19626954 T + 12200509765705829 T^{2} \)
$31$ \( 1 + 239950480 T + 25408476896404831 T^{2} \)
$37$ \( 1 - 488238078 T + 177917621779460413 T^{2} \)
$41$ \( 1 - 47066010 T + 550329031716248441 T^{2} \)
$43$ \( 1 - 428866948 T + 929293739471222707 T^{2} \)
$47$ \( 1 - 450903216 T + 2472159215084012303 T^{2} \)
$53$ \( 1 - 4336685950 T + 9269035929372191597 T^{2} \)
$59$ \( 1 + 8937556460 T + 30155888444737842659 T^{2} \)
$61$ \( 1 - 4673884486 T + 43513917611435838661 T^{2} \)
$67$ \( 1 - 7498937612 T + \)\(12\!\cdots\!83\)\( T^{2} \)
$71$ \( 1 + 27032101480 T + \)\(23\!\cdots\!71\)\( T^{2} \)
$73$ \( 1 - 11676141658 T + \)\(31\!\cdots\!77\)\( T^{2} \)
$79$ \( 1 - 2478876544 T + \)\(74\!\cdots\!79\)\( T^{2} \)
$83$ \( 1 - 42745596956 T + \)\(12\!\cdots\!67\)\( T^{2} \)
$89$ \( 1 + 93270772662 T + \)\(27\!\cdots\!89\)\( T^{2} \)
$97$ \( 1 - 118032786914 T + \)\(71\!\cdots\!53\)\( T^{2} \)
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