Properties

Label 4650.2.a.bj
Level $4650$
Weight $2$
Character orbit 4650.a
Self dual yes
Analytic conductor $37.130$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.1304369399\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 3 q^{7} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} + q^{4} + q^{6} - 3 q^{7} + q^{8} + q^{9} - q^{11} + q^{12} + 3 q^{13} - 3 q^{14} + q^{16} - 4 q^{17} + q^{18} - 2 q^{19} - 3 q^{21} - q^{22} + 4 q^{23} + q^{24} + 3 q^{26} + q^{27} - 3 q^{28} + 6 q^{29} - q^{31} + q^{32} - q^{33} - 4 q^{34} + q^{36} + 7 q^{37} - 2 q^{38} + 3 q^{39} + 7 q^{41} - 3 q^{42} + 11 q^{43} - q^{44} + 4 q^{46} + 3 q^{47} + q^{48} + 2 q^{49} - 4 q^{51} + 3 q^{52} + 5 q^{53} + q^{54} - 3 q^{56} - 2 q^{57} + 6 q^{58} + 6 q^{59} + q^{61} - q^{62} - 3 q^{63} + q^{64} - q^{66} + 14 q^{67} - 4 q^{68} + 4 q^{69} - 9 q^{71} + q^{72} + 2 q^{73} + 7 q^{74} - 2 q^{76} + 3 q^{77} + 3 q^{78} + q^{81} + 7 q^{82} + q^{83} - 3 q^{84} + 11 q^{86} + 6 q^{87} - q^{88} + 10 q^{89} - 9 q^{91} + 4 q^{92} - q^{93} + 3 q^{94} + q^{96} + 6 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 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
1.00000 1.00000 1.00000 0 1.00000 −3.00000 1.00000 1.00000 0
\(n\): 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 4650.2.a.bj yes 1
5.b even 2 1 4650.2.a.l 1
5.c odd 4 2 4650.2.d.t 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4650.2.a.l 1 5.b even 2 1
4650.2.a.bj yes 1 1.a even 1 1 trivial
4650.2.d.t 2 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4650))\):

\( T_{7} + 3 \) Copy content Toggle raw display
\( T_{11} + 1 \) Copy content Toggle raw display
\( T_{13} - 3 \) Copy content Toggle raw display
\( T_{19} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T + 1 \) Copy content Toggle raw display
$13$ \( T - 3 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T + 2 \) Copy content Toggle raw display
$23$ \( T - 4 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T + 1 \) Copy content Toggle raw display
$37$ \( T - 7 \) Copy content Toggle raw display
$41$ \( T - 7 \) Copy content Toggle raw display
$43$ \( T - 11 \) Copy content Toggle raw display
$47$ \( T - 3 \) Copy content Toggle raw display
$53$ \( T - 5 \) Copy content Toggle raw display
$59$ \( T - 6 \) Copy content Toggle raw display
$61$ \( T - 1 \) Copy content Toggle raw display
$67$ \( T - 14 \) Copy content Toggle raw display
$71$ \( T + 9 \) Copy content Toggle raw display
$73$ \( T - 2 \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T - 1 \) Copy content Toggle raw display
$89$ \( T - 10 \) Copy content Toggle raw display
$97$ \( T - 6 \) Copy content Toggle raw display
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