Properties

Label 2394.4.a.c
Level $2394$
Weight $4$
Character orbit 2394.a
Self dual yes
Analytic conductor $141.251$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(141.250572554\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 798)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{2} + 4 q^{4} + 10 q^{5} + 7 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 4 q^{4} + 10 q^{5} + 7 q^{7} - 8 q^{8} - 20 q^{10} - 8 q^{11} - 50 q^{13} - 14 q^{14} + 16 q^{16} - 114 q^{17} + 19 q^{19} + 40 q^{20} + 16 q^{22} + 148 q^{23} - 25 q^{25} + 100 q^{26} + 28 q^{28} + 30 q^{29} + 304 q^{31} - 32 q^{32} + 228 q^{34} + 70 q^{35} - 274 q^{37} - 38 q^{38} - 80 q^{40} + 202 q^{41} - 116 q^{43} - 32 q^{44} - 296 q^{46} + 324 q^{47} + 49 q^{49} + 50 q^{50} - 200 q^{52} + 550 q^{53} - 80 q^{55} - 56 q^{56} - 60 q^{58} - 628 q^{59} - 58 q^{61} - 608 q^{62} + 64 q^{64} - 500 q^{65} - 756 q^{67} - 456 q^{68} - 140 q^{70} + 216 q^{71} - 278 q^{73} + 548 q^{74} + 76 q^{76} - 56 q^{77} - 952 q^{79} + 160 q^{80} - 404 q^{82} + 1184 q^{83} - 1140 q^{85} + 232 q^{86} + 64 q^{88} - 1542 q^{89} - 350 q^{91} + 592 q^{92} - 648 q^{94} + 190 q^{95} - 870 q^{97} - 98 q^{98}+O(q^{100}) \) 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
−2.00000 0 4.00000 10.0000 0 7.00000 −8.00000 0 −20.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(7\) \(-1\)
\(19\) \(-1\)

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 2394.4.a.c 1
3.b odd 2 1 798.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
798.4.a.b 1 3.b odd 2 1
2394.4.a.c 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2394))\):

\( T_{5} - 10 \) Copy content Toggle raw display
\( T_{11} + 8 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 10 \) Copy content Toggle raw display
$7$ \( T - 7 \) Copy content Toggle raw display
$11$ \( T + 8 \) Copy content Toggle raw display
$13$ \( T + 50 \) Copy content Toggle raw display
$17$ \( T + 114 \) Copy content Toggle raw display
$19$ \( T - 19 \) Copy content Toggle raw display
$23$ \( T - 148 \) Copy content Toggle raw display
$29$ \( T - 30 \) Copy content Toggle raw display
$31$ \( T - 304 \) Copy content Toggle raw display
$37$ \( T + 274 \) Copy content Toggle raw display
$41$ \( T - 202 \) Copy content Toggle raw display
$43$ \( T + 116 \) Copy content Toggle raw display
$47$ \( T - 324 \) Copy content Toggle raw display
$53$ \( T - 550 \) Copy content Toggle raw display
$59$ \( T + 628 \) Copy content Toggle raw display
$61$ \( T + 58 \) Copy content Toggle raw display
$67$ \( T + 756 \) Copy content Toggle raw display
$71$ \( T - 216 \) Copy content Toggle raw display
$73$ \( T + 278 \) Copy content Toggle raw display
$79$ \( T + 952 \) Copy content Toggle raw display
$83$ \( T - 1184 \) Copy content Toggle raw display
$89$ \( T + 1542 \) Copy content Toggle raw display
$97$ \( T + 870 \) Copy content Toggle raw display
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