Properties

Label 230.4.a.d
Level $230$
Weight $4$
Character orbit 230.a
Self dual yes
Analytic conductor $13.570$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.5704393013\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} - q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 32 q^{7} + 8 q^{8} - 26 q^{9} + O(q^{10}) \) \( q + 2 q^{2} - q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 32 q^{7} + 8 q^{8} - 26 q^{9} + 10 q^{10} - 30 q^{11} - 4 q^{12} + 19 q^{13} - 64 q^{14} - 5 q^{15} + 16 q^{16} - 60 q^{17} - 52 q^{18} - 58 q^{19} + 20 q^{20} + 32 q^{21} - 60 q^{22} + 23 q^{23} - 8 q^{24} + 25 q^{25} + 38 q^{26} + 53 q^{27} - 128 q^{28} + 85 q^{29} - 10 q^{30} - 65 q^{31} + 32 q^{32} + 30 q^{33} - 120 q^{34} - 160 q^{35} - 104 q^{36} - 34 q^{37} - 116 q^{38} - 19 q^{39} + 40 q^{40} + 143 q^{41} + 64 q^{42} - 332 q^{43} - 120 q^{44} - 130 q^{45} + 46 q^{46} - 561 q^{47} - 16 q^{48} + 681 q^{49} + 50 q^{50} + 60 q^{51} + 76 q^{52} - 422 q^{53} + 106 q^{54} - 150 q^{55} - 256 q^{56} + 58 q^{57} + 170 q^{58} + 392 q^{59} - 20 q^{60} - 246 q^{61} - 130 q^{62} + 832 q^{63} + 64 q^{64} + 95 q^{65} + 60 q^{66} + 894 q^{67} - 240 q^{68} - 23 q^{69} - 320 q^{70} - 737 q^{71} - 208 q^{72} + 1041 q^{73} - 68 q^{74} - 25 q^{75} - 232 q^{76} + 960 q^{77} - 38 q^{78} + 1114 q^{79} + 80 q^{80} + 649 q^{81} + 286 q^{82} - 936 q^{83} + 128 q^{84} - 300 q^{85} - 664 q^{86} - 85 q^{87} - 240 q^{88} + 824 q^{89} - 260 q^{90} - 608 q^{91} + 92 q^{92} + 65 q^{93} - 1122 q^{94} - 290 q^{95} - 32 q^{96} - 868 q^{97} + 1362 q^{98} + 780 q^{99} + O(q^{100}) \)

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
2.00000 −1.00000 4.00000 5.00000 −2.00000 −32.0000 8.00000 −26.0000 10.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(23\) \(-1\)

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 230.4.a.d 1
3.b odd 2 1 2070.4.a.a 1
4.b odd 2 1 1840.4.a.e 1
5.b even 2 1 1150.4.a.c 1
5.c odd 4 2 1150.4.b.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.d 1 1.a even 1 1 trivial
1150.4.a.c 1 5.b even 2 1
1150.4.b.d 2 5.c odd 4 2
1840.4.a.e 1 4.b odd 2 1
2070.4.a.a 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(230))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( 1 + T \)
$5$ \( -5 + T \)
$7$ \( 32 + T \)
$11$ \( 30 + T \)
$13$ \( -19 + T \)
$17$ \( 60 + T \)
$19$ \( 58 + T \)
$23$ \( -23 + T \)
$29$ \( -85 + T \)
$31$ \( 65 + T \)
$37$ \( 34 + T \)
$41$ \( -143 + T \)
$43$ \( 332 + T \)
$47$ \( 561 + T \)
$53$ \( 422 + T \)
$59$ \( -392 + T \)
$61$ \( 246 + T \)
$67$ \( -894 + T \)
$71$ \( 737 + T \)
$73$ \( -1041 + T \)
$79$ \( -1114 + T \)
$83$ \( 936 + T \)
$89$ \( -824 + T \)
$97$ \( 868 + T \)
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