Properties

Label 930.2.a.a
Level $930$
Weight $2$
Character orbit 930.a
Self dual yes
Analytic conductor $7.426$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 3q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 3q^{7} - q^{8} + q^{9} + q^{10} + 3q^{11} - q^{12} - 2q^{13} + 3q^{14} + q^{15} + q^{16} - 4q^{17} - q^{18} - 3q^{19} - q^{20} + 3q^{21} - 3q^{22} + 5q^{23} + q^{24} + q^{25} + 2q^{26} - q^{27} - 3q^{28} + 4q^{29} - q^{30} + q^{31} - q^{32} - 3q^{33} + 4q^{34} + 3q^{35} + q^{36} + 3q^{38} + 2q^{39} + q^{40} + 4q^{41} - 3q^{42} + q^{43} + 3q^{44} - q^{45} - 5q^{46} + 10q^{47} - q^{48} + 2q^{49} - q^{50} + 4q^{51} - 2q^{52} + 3q^{53} + q^{54} - 3q^{55} + 3q^{56} + 3q^{57} - 4q^{58} + 6q^{59} + q^{60} - 2q^{61} - q^{62} - 3q^{63} + q^{64} + 2q^{65} + 3q^{66} + 2q^{67} - 4q^{68} - 5q^{69} - 3q^{70} + 7q^{71} - q^{72} + 5q^{73} - q^{75} - 3q^{76} - 9q^{77} - 2q^{78} - q^{79} - q^{80} + q^{81} - 4q^{82} + 12q^{83} + 3q^{84} + 4q^{85} - q^{86} - 4q^{87} - 3q^{88} + q^{89} + q^{90} + 6q^{91} + 5q^{92} - q^{93} - 10q^{94} + 3q^{95} + q^{96} - 10q^{97} - 2q^{98} + 3q^{99} + O(q^{100}) \)

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 −1.00000 1.00000 −1.00000 1.00000 −3.00000 −1.00000 1.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(5\) \(1\)
\(31\) \(-1\)

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 930.2.a.a 1
3.b odd 2 1 2790.2.a.y 1
4.b odd 2 1 7440.2.a.v 1
5.b even 2 1 4650.2.a.bv 1
5.c odd 4 2 4650.2.d.y 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.a.a 1 1.a even 1 1 trivial
2790.2.a.y 1 3.b odd 2 1
4650.2.a.bv 1 5.b even 2 1
4650.2.d.y 2 5.c odd 4 2
7440.2.a.v 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(930))\):

\( T_{7} + 3 \)
\( T_{11} - 3 \)
\( T_{19} + 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( 3 + T \)
$11$ \( -3 + T \)
$13$ \( 2 + T \)
$17$ \( 4 + T \)
$19$ \( 3 + T \)
$23$ \( -5 + T \)
$29$ \( -4 + T \)
$31$ \( -1 + T \)
$37$ \( T \)
$41$ \( -4 + T \)
$43$ \( -1 + T \)
$47$ \( -10 + T \)
$53$ \( -3 + T \)
$59$ \( -6 + T \)
$61$ \( 2 + T \)
$67$ \( -2 + T \)
$71$ \( -7 + T \)
$73$ \( -5 + T \)
$79$ \( 1 + T \)
$83$ \( -12 + T \)
$89$ \( -1 + T \)
$97$ \( 10 + T \)
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