Properties

Label 24.12.a.b
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

Related objects

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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

\(f(q)\) \(=\) \( q - 243q^{3} + 1190q^{5} + 18480q^{7} + 59049q^{9} + O(q^{10}) \) \( q - 243q^{3} + 1190q^{5} + 18480q^{7} + 59049q^{9} + 135884q^{11} - 848186q^{13} - 289170q^{15} - 7124606q^{17} - 5046316q^{19} - 4490640q^{21} - 14891224q^{23} - 47412025q^{25} - 14348907q^{27} - 115001346q^{29} - 163990552q^{31} - 33019812q^{33} + 21991200q^{35} - 223622178q^{37} + 206109198q^{39} + 105358314q^{41} + 1419475852q^{43} + 70268310q^{45} + 2469276960q^{47} - 1635816343q^{49} + 1731279258q^{51} - 483704986q^{53} + 161701960q^{55} + 1226254788q^{57} + 6151842476q^{59} - 7532732282q^{61} + 1091225520q^{63} - 1009341340q^{65} - 8764949068q^{67} + 3618567432q^{69} - 10401627752q^{71} - 31738391270q^{73} + 11521122075q^{75} + 2511136320q^{77} - 39880016072q^{79} + 3486784401q^{81} + 13513323988q^{83} - 8478281140q^{85} + 27945327078q^{87} + 81514517226q^{89} - 15674477280q^{91} + 39849704136q^{93} - 6005116040q^{95} + 30783027074q^{97} + 8023814316q^{99} + O(q^{100}) \)

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 1190.00 0 18480.0 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.b 1
3.b odd 2 1 72.12.a.b 1
4.b odd 2 1 48.12.a.g 1
8.b even 2 1 192.12.a.p 1
8.d odd 2 1 192.12.a.f 1
12.b even 2 1 144.12.a.h 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.12.a.b 1 1.a even 1 1 trivial
48.12.a.g 1 4.b odd 2 1
72.12.a.b 1 3.b odd 2 1
144.12.a.h 1 12.b even 2 1
192.12.a.f 1 8.d odd 2 1
192.12.a.p 1 8.b even 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 \( T_{5} - 1190 \) acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(24))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 + 243 T \)
$5$ \( 1 - 1190 T + 48828125 T^{2} \)
$7$ \( 1 - 18480 T + 1977326743 T^{2} \)
$11$ \( 1 - 135884 T + 285311670611 T^{2} \)
$13$ \( 1 + 848186 T + 1792160394037 T^{2} \)
$17$ \( 1 + 7124606 T + 34271896307633 T^{2} \)
$19$ \( 1 + 5046316 T + 116490258898219 T^{2} \)
$23$ \( 1 + 14891224 T + 952809757913927 T^{2} \)
$29$ \( 1 + 115001346 T + 12200509765705829 T^{2} \)
$31$ \( 1 + 163990552 T + 25408476896404831 T^{2} \)
$37$ \( 1 + 223622178 T + 177917621779460413 T^{2} \)
$41$ \( 1 - 105358314 T + 550329031716248441 T^{2} \)
$43$ \( 1 - 1419475852 T + 929293739471222707 T^{2} \)
$47$ \( 1 - 2469276960 T + 2472159215084012303 T^{2} \)
$53$ \( 1 + 483704986 T + 9269035929372191597 T^{2} \)
$59$ \( 1 - 6151842476 T + 30155888444737842659 T^{2} \)
$61$ \( 1 + 7532732282 T + 43513917611435838661 T^{2} \)
$67$ \( 1 + 8764949068 T + \)\(12\!\cdots\!83\)\( T^{2} \)
$71$ \( 1 + 10401627752 T + \)\(23\!\cdots\!71\)\( T^{2} \)
$73$ \( 1 + 31738391270 T + \)\(31\!\cdots\!77\)\( T^{2} \)
$79$ \( 1 + 39880016072 T + \)\(74\!\cdots\!79\)\( T^{2} \)
$83$ \( 1 - 13513323988 T + \)\(12\!\cdots\!67\)\( T^{2} \)
$89$ \( 1 - 81514517226 T + \)\(27\!\cdots\!89\)\( T^{2} \)
$97$ \( 1 - 30783027074 T + \)\(71\!\cdots\!53\)\( T^{2} \)
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