Properties

Label 430.2.a.c
Level 430
Weight 2
Character orbit 430.a
Self dual yes
Analytic conductor 3.434
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 430.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.43356728692\)
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

\(f(q)\) \(=\) \( q + q^{2} - 2q^{3} + q^{4} - q^{5} - 2q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - 2q^{3} + q^{4} - q^{5} - 2q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - 6q^{11} - 2q^{12} + 5q^{13} - q^{14} + 2q^{15} + q^{16} - 6q^{17} + q^{18} - 7q^{19} - q^{20} + 2q^{21} - 6q^{22} - 6q^{23} - 2q^{24} + q^{25} + 5q^{26} + 4q^{27} - q^{28} - 3q^{29} + 2q^{30} + 5q^{31} + q^{32} + 12q^{33} - 6q^{34} + q^{35} + q^{36} + 2q^{37} - 7q^{38} - 10q^{39} - q^{40} - 3q^{41} + 2q^{42} + q^{43} - 6q^{44} - q^{45} - 6q^{46} + 12q^{47} - 2q^{48} - 6q^{49} + q^{50} + 12q^{51} + 5q^{52} + 6q^{53} + 4q^{54} + 6q^{55} - q^{56} + 14q^{57} - 3q^{58} - 12q^{59} + 2q^{60} - q^{61} + 5q^{62} - q^{63} + q^{64} - 5q^{65} + 12q^{66} - 13q^{67} - 6q^{68} + 12q^{69} + q^{70} + 12q^{71} + q^{72} + 11q^{73} + 2q^{74} - 2q^{75} - 7q^{76} + 6q^{77} - 10q^{78} - q^{79} - q^{80} - 11q^{81} - 3q^{82} + 2q^{84} + 6q^{85} + q^{86} + 6q^{87} - 6q^{88} + 6q^{89} - q^{90} - 5q^{91} - 6q^{92} - 10q^{93} + 12q^{94} + 7q^{95} - 2q^{96} + 8q^{97} - 6q^{98} - 6q^{99} + O(q^{100}) \)

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
1.00000 −2.00000 1.00000 −1.00000 −2.00000 −1.00000 1.00000 1.00000 −1.00000
\(n\): 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 430.2.a.c 1
3.b odd 2 1 3870.2.a.h 1
4.b odd 2 1 3440.2.a.d 1
5.b even 2 1 2150.2.a.f 1
5.c odd 4 2 2150.2.b.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
430.2.a.c 1 1.a even 1 1 trivial
2150.2.a.f 1 5.b even 2 1
2150.2.b.c 2 5.c odd 4 2
3440.2.a.d 1 4.b odd 2 1
3870.2.a.h 1 3.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(43\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(430))\):

\( T_{3} + 2 \)
\( T_{7} + 1 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ \( 1 + 2 T + 3 T^{2} \)
$5$ \( 1 + T \)
$7$ \( 1 + T + 7 T^{2} \)
$11$ \( 1 + 6 T + 11 T^{2} \)
$13$ \( 1 - 5 T + 13 T^{2} \)
$17$ \( 1 + 6 T + 17 T^{2} \)
$19$ \( 1 + 7 T + 19 T^{2} \)
$23$ \( 1 + 6 T + 23 T^{2} \)
$29$ \( 1 + 3 T + 29 T^{2} \)
$31$ \( 1 - 5 T + 31 T^{2} \)
$37$ \( 1 - 2 T + 37 T^{2} \)
$41$ \( 1 + 3 T + 41 T^{2} \)
$43$ \( 1 - T \)
$47$ \( 1 - 12 T + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 + 12 T + 59 T^{2} \)
$61$ \( 1 + T + 61 T^{2} \)
$67$ \( 1 + 13 T + 67 T^{2} \)
$71$ \( 1 - 12 T + 71 T^{2} \)
$73$ \( 1 - 11 T + 73 T^{2} \)
$79$ \( 1 + T + 79 T^{2} \)
$83$ \( 1 + 83 T^{2} \)
$89$ \( 1 - 6 T + 89 T^{2} \)
$97$ \( 1 - 8 T + 97 T^{2} \)
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