Properties

Label 46.4.a.a
Level $46$
Weight $4$
Character orbit 46.a
Self dual yes
Analytic conductor $2.714$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 46.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.71408786026\)
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

\(f(q)\) \(=\) \( q - 2 q^{2} - q^{3} + 4 q^{4} - 10 q^{5} + 2 q^{6} - 12 q^{7} - 8 q^{8} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} - q^{3} + 4 q^{4} - 10 q^{5} + 2 q^{6} - 12 q^{7} - 8 q^{8} - 26 q^{9} + 20 q^{10} - 42 q^{11} - 4 q^{12} + 7 q^{13} + 24 q^{14} + 10 q^{15} + 16 q^{16} + 20 q^{17} + 52 q^{18} + 106 q^{19} - 40 q^{20} + 12 q^{21} + 84 q^{22} + 23 q^{23} + 8 q^{24} - 25 q^{25} - 14 q^{26} + 53 q^{27} - 48 q^{28} - 227 q^{29} - 20 q^{30} + 67 q^{31} - 32 q^{32} + 42 q^{33} - 40 q^{34} + 120 q^{35} - 104 q^{36} + 74 q^{37} - 212 q^{38} - 7 q^{39} + 80 q^{40} - 497 q^{41} - 24 q^{42} - 88 q^{43} - 168 q^{44} + 260 q^{45} - 46 q^{46} + 215 q^{47} - 16 q^{48} - 199 q^{49} + 50 q^{50} - 20 q^{51} + 28 q^{52} + 314 q^{53} - 106 q^{54} + 420 q^{55} + 96 q^{56} - 106 q^{57} + 454 q^{58} + 176 q^{59} + 40 q^{60} - 298 q^{61} - 134 q^{62} + 312 q^{63} + 64 q^{64} - 70 q^{65} - 84 q^{66} + 266 q^{67} + 80 q^{68} - 23 q^{69} - 240 q^{70} - 981 q^{71} + 208 q^{72} - 411 q^{73} - 148 q^{74} + 25 q^{75} + 424 q^{76} + 504 q^{77} + 14 q^{78} + 806 q^{79} - 160 q^{80} + 649 q^{81} + 994 q^{82} - 952 q^{83} + 48 q^{84} - 200 q^{85} + 176 q^{86} + 227 q^{87} + 336 q^{88} - 1332 q^{89} - 520 q^{90} - 84 q^{91} + 92 q^{92} - 67 q^{93} - 430 q^{94} - 1060 q^{95} + 32 q^{96} - 1328 q^{97} + 398 q^{98} + 1092 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
−2.00000 −1.00000 4.00000 −10.0000 2.00000 −12.0000 −8.00000 −26.0000 20.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(23\) \(-1\)

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 46.4.a.a 1
3.b odd 2 1 414.4.a.d 1
4.b odd 2 1 368.4.a.b 1
5.b even 2 1 1150.4.a.g 1
5.c odd 4 2 1150.4.b.e 2
7.b odd 2 1 2254.4.a.a 1
8.b even 2 1 1472.4.a.f 1
8.d odd 2 1 1472.4.a.e 1
23.b odd 2 1 1058.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.4.a.a 1 1.a even 1 1 trivial
368.4.a.b 1 4.b odd 2 1
414.4.a.d 1 3.b odd 2 1
1058.4.a.a 1 23.b odd 2 1
1150.4.a.g 1 5.b even 2 1
1150.4.b.e 2 5.c odd 4 2
1472.4.a.e 1 8.d odd 2 1
1472.4.a.f 1 8.b even 2 1
2254.4.a.a 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(46))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T + 10 \) Copy content Toggle raw display
$7$ \( T + 12 \) Copy content Toggle raw display
$11$ \( T + 42 \) Copy content Toggle raw display
$13$ \( T - 7 \) Copy content Toggle raw display
$17$ \( T - 20 \) Copy content Toggle raw display
$19$ \( T - 106 \) Copy content Toggle raw display
$23$ \( T - 23 \) Copy content Toggle raw display
$29$ \( T + 227 \) Copy content Toggle raw display
$31$ \( T - 67 \) Copy content Toggle raw display
$37$ \( T - 74 \) Copy content Toggle raw display
$41$ \( T + 497 \) Copy content Toggle raw display
$43$ \( T + 88 \) Copy content Toggle raw display
$47$ \( T - 215 \) Copy content Toggle raw display
$53$ \( T - 314 \) Copy content Toggle raw display
$59$ \( T - 176 \) Copy content Toggle raw display
$61$ \( T + 298 \) Copy content Toggle raw display
$67$ \( T - 266 \) Copy content Toggle raw display
$71$ \( T + 981 \) Copy content Toggle raw display
$73$ \( T + 411 \) Copy content Toggle raw display
$79$ \( T - 806 \) Copy content Toggle raw display
$83$ \( T + 952 \) Copy content Toggle raw display
$89$ \( T + 1332 \) Copy content Toggle raw display
$97$ \( T + 1328 \) Copy content Toggle raw display
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