Properties

Label 798.4.a.b
Level $798$
Weight $4$
Character orbit 798.a
Self dual yes
Analytic conductor $47.084$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 798.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.0835241846\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 10 q^{5} - 6 q^{6} + 7 q^{7} + 8 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 10 q^{5} - 6 q^{6} + 7 q^{7} + 8 q^{8} + 9 q^{9} - 20 q^{10} + 8 q^{11} - 12 q^{12} - 50 q^{13} + 14 q^{14} + 30 q^{15} + 16 q^{16} + 114 q^{17} + 18 q^{18} + 19 q^{19} - 40 q^{20} - 21 q^{21} + 16 q^{22} - 148 q^{23} - 24 q^{24} - 25 q^{25} - 100 q^{26} - 27 q^{27} + 28 q^{28} - 30 q^{29} + 60 q^{30} + 304 q^{31} + 32 q^{32} - 24 q^{33} + 228 q^{34} - 70 q^{35} + 36 q^{36} - 274 q^{37} + 38 q^{38} + 150 q^{39} - 80 q^{40} - 202 q^{41} - 42 q^{42} - 116 q^{43} + 32 q^{44} - 90 q^{45} - 296 q^{46} - 324 q^{47} - 48 q^{48} + 49 q^{49} - 50 q^{50} - 342 q^{51} - 200 q^{52} - 550 q^{53} - 54 q^{54} - 80 q^{55} + 56 q^{56} - 57 q^{57} - 60 q^{58} + 628 q^{59} + 120 q^{60} - 58 q^{61} + 608 q^{62} + 63 q^{63} + 64 q^{64} + 500 q^{65} - 48 q^{66} - 756 q^{67} + 456 q^{68} + 444 q^{69} - 140 q^{70} - 216 q^{71} + 72 q^{72} - 278 q^{73} - 548 q^{74} + 75 q^{75} + 76 q^{76} + 56 q^{77} + 300 q^{78} - 952 q^{79} - 160 q^{80} + 81 q^{81} - 404 q^{82} - 1184 q^{83} - 84 q^{84} - 1140 q^{85} - 232 q^{86} + 90 q^{87} + 64 q^{88} + 1542 q^{89} - 180 q^{90} - 350 q^{91} - 592 q^{92} - 912 q^{93} - 648 q^{94} - 190 q^{95} - 96 q^{96} - 870 q^{97} + 98 q^{98} + 72 q^{99}+O(q^{100}) \) 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
2.00000 −3.00000 4.00000 −10.0000 −6.00000 7.00000 8.00000 9.00000 −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 798.4.a.b 1
3.b odd 2 1 2394.4.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
798.4.a.b 1 1.a even 1 1 trivial
2394.4.a.c 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} + 10 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(798))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) Copy content Toggle raw display
$3$ \( T + 3 \) 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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