Properties

Label 46.4.a.b
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

\(f(q)\) \(=\) \( q + 2 q^{2} - 9 q^{3} + 4 q^{4} - 20 q^{5} - 18 q^{6} + 2 q^{7} + 8 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - 9 q^{3} + 4 q^{4} - 20 q^{5} - 18 q^{6} + 2 q^{7} + 8 q^{8} + 54 q^{9} - 40 q^{10} - 52 q^{11} - 36 q^{12} + 43 q^{13} + 4 q^{14} + 180 q^{15} + 16 q^{16} - 50 q^{17} + 108 q^{18} - 74 q^{19} - 80 q^{20} - 18 q^{21} - 104 q^{22} - 23 q^{23} - 72 q^{24} + 275 q^{25} + 86 q^{26} - 243 q^{27} + 8 q^{28} - 7 q^{29} + 360 q^{30} - 273 q^{31} + 32 q^{32} + 468 q^{33} - 100 q^{34} - 40 q^{35} + 216 q^{36} - 4 q^{37} - 148 q^{38} - 387 q^{39} - 160 q^{40} + 123 q^{41} - 36 q^{42} - 152 q^{43} - 208 q^{44} - 1080 q^{45} - 46 q^{46} + 75 q^{47} - 144 q^{48} - 339 q^{49} + 550 q^{50} + 450 q^{51} + 172 q^{52} + 86 q^{53} - 486 q^{54} + 1040 q^{55} + 16 q^{56} + 666 q^{57} - 14 q^{58} - 444 q^{59} + 720 q^{60} + 262 q^{61} - 546 q^{62} + 108 q^{63} + 64 q^{64} - 860 q^{65} + 936 q^{66} + 764 q^{67} - 200 q^{68} + 207 q^{69} - 80 q^{70} - 21 q^{71} + 432 q^{72} + 681 q^{73} - 8 q^{74} - 2475 q^{75} - 296 q^{76} - 104 q^{77} - 774 q^{78} + 426 q^{79} - 320 q^{80} + 729 q^{81} + 246 q^{82} + 902 q^{83} - 72 q^{84} + 1000 q^{85} - 304 q^{86} + 63 q^{87} - 416 q^{88} - 1272 q^{89} - 2160 q^{90} + 86 q^{91} - 92 q^{92} + 2457 q^{93} + 150 q^{94} + 1480 q^{95} - 288 q^{96} - 342 q^{97} - 678 q^{98} - 2808 q^{99}+O(q^{100}) \) 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 −9.00000 4.00000 −20.0000 −18.0000 2.00000 8.00000 54.0000 −40.0000
\(n\): 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.b 1
3.b odd 2 1 414.4.a.b 1
4.b odd 2 1 368.4.a.e 1
5.b even 2 1 1150.4.a.d 1
5.c odd 4 2 1150.4.b.a 2
7.b odd 2 1 2254.4.a.b 1
8.b even 2 1 1472.4.a.j 1
8.d odd 2 1 1472.4.a.a 1
23.b odd 2 1 1058.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.4.a.b 1 1.a even 1 1 trivial
368.4.a.e 1 4.b odd 2 1
414.4.a.b 1 3.b odd 2 1
1058.4.a.b 1 23.b odd 2 1
1150.4.a.d 1 5.b even 2 1
1150.4.b.a 2 5.c odd 4 2
1472.4.a.a 1 8.d odd 2 1
1472.4.a.j 1 8.b even 2 1
2254.4.a.b 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 9 \) 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
$3$ \( T + 9 \) Copy content Toggle raw display
$5$ \( T + 20 \) Copy content Toggle raw display
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T + 52 \) Copy content Toggle raw display
$13$ \( T - 43 \) Copy content Toggle raw display
$17$ \( T + 50 \) Copy content Toggle raw display
$19$ \( T + 74 \) Copy content Toggle raw display
$23$ \( T + 23 \) Copy content Toggle raw display
$29$ \( T + 7 \) Copy content Toggle raw display
$31$ \( T + 273 \) Copy content Toggle raw display
$37$ \( T + 4 \) Copy content Toggle raw display
$41$ \( T - 123 \) Copy content Toggle raw display
$43$ \( T + 152 \) Copy content Toggle raw display
$47$ \( T - 75 \) Copy content Toggle raw display
$53$ \( T - 86 \) Copy content Toggle raw display
$59$ \( T + 444 \) Copy content Toggle raw display
$61$ \( T - 262 \) Copy content Toggle raw display
$67$ \( T - 764 \) Copy content Toggle raw display
$71$ \( T + 21 \) Copy content Toggle raw display
$73$ \( T - 681 \) Copy content Toggle raw display
$79$ \( T - 426 \) Copy content Toggle raw display
$83$ \( T - 902 \) Copy content Toggle raw display
$89$ \( T + 1272 \) Copy content Toggle raw display
$97$ \( T + 342 \) Copy content Toggle raw display
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