Properties

Label 230.4.a.a
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

\(f(q)\) \(=\) \( q - 2q^{2} - 5q^{3} + 4q^{4} - 5q^{5} + 10q^{6} + 12q^{7} - 8q^{8} - 2q^{9} + O(q^{10}) \) \( q - 2q^{2} - 5q^{3} + 4q^{4} - 5q^{5} + 10q^{6} + 12q^{7} - 8q^{8} - 2q^{9} + 10q^{10} + 22q^{11} - 20q^{12} + 19q^{13} - 24q^{14} + 25q^{15} + 16q^{16} + 96q^{17} + 4q^{18} - 98q^{19} - 20q^{20} - 60q^{21} - 44q^{22} + 23q^{23} + 40q^{24} + 25q^{25} - 38q^{26} + 145q^{27} + 48q^{28} - 227q^{29} - 50q^{30} - 285q^{31} - 32q^{32} - 110q^{33} - 192q^{34} - 60q^{35} - 8q^{36} - 398q^{37} + 196q^{38} - 95q^{39} + 40q^{40} + 271q^{41} + 120q^{42} - 100q^{43} + 88q^{44} + 10q^{45} - 46q^{46} - 285q^{47} - 80q^{48} - 199q^{49} - 50q^{50} - 480q^{51} + 76q^{52} + 18q^{53} - 290q^{54} - 110q^{55} - 96q^{56} + 490q^{57} + 454q^{58} - 352q^{59} + 100q^{60} - 478q^{61} + 570q^{62} - 24q^{63} + 64q^{64} - 95q^{65} + 220q^{66} + 330q^{67} + 384q^{68} - 115q^{69} + 120q^{70} + 835q^{71} + 16q^{72} - 1127q^{73} + 796q^{74} - 125q^{75} - 392q^{76} + 264q^{77} + 190q^{78} + 322q^{79} - 80q^{80} - 671q^{81} - 542q^{82} + 572q^{83} - 240q^{84} - 480q^{85} + 200q^{86} + 1135q^{87} - 176q^{88} - 504q^{89} - 20q^{90} + 228q^{91} + 92q^{92} + 1425q^{93} + 570q^{94} + 490q^{95} + 160q^{96} + 1712q^{97} + 398q^{98} - 44q^{99} + O(q^{100}) \)

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 −5.00000 4.00000 −5.00000 10.0000 12.0000 −8.00000 −2.00000 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.a 1
3.b odd 2 1 2070.4.a.o 1
4.b odd 2 1 1840.4.a.g 1
5.b even 2 1 1150.4.a.i 1
5.c odd 4 2 1150.4.b.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.a 1 1.a even 1 1 trivial
1150.4.a.i 1 5.b even 2 1
1150.4.b.h 2 5.c odd 4 2
1840.4.a.g 1 4.b odd 2 1
2070.4.a.o 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 5 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(230))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( 5 + T \)
$5$ \( 5 + T \)
$7$ \( -12 + T \)
$11$ \( -22 + T \)
$13$ \( -19 + T \)
$17$ \( -96 + T \)
$19$ \( 98 + T \)
$23$ \( -23 + T \)
$29$ \( 227 + T \)
$31$ \( 285 + T \)
$37$ \( 398 + T \)
$41$ \( -271 + T \)
$43$ \( 100 + T \)
$47$ \( 285 + T \)
$53$ \( -18 + T \)
$59$ \( 352 + T \)
$61$ \( 478 + T \)
$67$ \( -330 + T \)
$71$ \( -835 + T \)
$73$ \( 1127 + T \)
$79$ \( -322 + T \)
$83$ \( -572 + T \)
$89$ \( 504 + T \)
$97$ \( -1712 + T \)
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