Properties

Label 930.4.a.c
Level $930$
Weight $4$
Character orbit 930.a
Self dual yes
Analytic conductor $54.872$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.8717763053\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} + 3 q^{3} + 4 q^{4} - 5 q^{5} + 6 q^{6} + 26 q^{7} + 8 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} + 3 q^{3} + 4 q^{4} - 5 q^{5} + 6 q^{6} + 26 q^{7} + 8 q^{8} + 9 q^{9} - 10 q^{10} - 48 q^{11} + 12 q^{12} - 88 q^{13} + 52 q^{14} - 15 q^{15} + 16 q^{16} - 54 q^{17} + 18 q^{18} - 160 q^{19} - 20 q^{20} + 78 q^{21} - 96 q^{22} - 48 q^{23} + 24 q^{24} + 25 q^{25} - 176 q^{26} + 27 q^{27} + 104 q^{28} - 120 q^{29} - 30 q^{30} + 31 q^{31} + 32 q^{32} - 144 q^{33} - 108 q^{34} - 130 q^{35} + 36 q^{36} - 304 q^{37} - 320 q^{38} - 264 q^{39} - 40 q^{40} + 162 q^{41} + 156 q^{42} + 272 q^{43} - 192 q^{44} - 45 q^{45} - 96 q^{46} + 96 q^{47} + 48 q^{48} + 333 q^{49} + 50 q^{50} - 162 q^{51} - 352 q^{52} + 582 q^{53} + 54 q^{54} + 240 q^{55} + 208 q^{56} - 480 q^{57} - 240 q^{58} + 30 q^{59} - 60 q^{60} - 478 q^{61} + 62 q^{62} + 234 q^{63} + 64 q^{64} + 440 q^{65} - 288 q^{66} - 334 q^{67} - 216 q^{68} - 144 q^{69} - 260 q^{70} + 1062 q^{71} + 72 q^{72} + 212 q^{73} - 608 q^{74} + 75 q^{75} - 640 q^{76} - 1248 q^{77} - 528 q^{78} - 640 q^{79} - 80 q^{80} + 81 q^{81} + 324 q^{82} + 972 q^{83} + 312 q^{84} + 270 q^{85} + 544 q^{86} - 360 q^{87} - 384 q^{88} + 120 q^{89} - 90 q^{90} - 2288 q^{91} - 192 q^{92} + 93 q^{93} + 192 q^{94} + 800 q^{95} + 96 q^{96} + 86 q^{97} + 666 q^{98} - 432 q^{99}+O(q^{100}) \) 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 −5.00000 6.00000 26.0000 8.00000 9.00000 −10.0000
\(n\): 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 930.4.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.4.a.c 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} - 26 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(930))\). 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
$5$ \( T + 5 \) Copy content Toggle raw display
$7$ \( T - 26 \) Copy content Toggle raw display
$11$ \( T + 48 \) Copy content Toggle raw display
$13$ \( T + 88 \) Copy content Toggle raw display
$17$ \( T + 54 \) Copy content Toggle raw display
$19$ \( T + 160 \) Copy content Toggle raw display
$23$ \( T + 48 \) Copy content Toggle raw display
$29$ \( T + 120 \) Copy content Toggle raw display
$31$ \( T - 31 \) Copy content Toggle raw display
$37$ \( T + 304 \) Copy content Toggle raw display
$41$ \( T - 162 \) Copy content Toggle raw display
$43$ \( T - 272 \) Copy content Toggle raw display
$47$ \( T - 96 \) Copy content Toggle raw display
$53$ \( T - 582 \) Copy content Toggle raw display
$59$ \( T - 30 \) Copy content Toggle raw display
$61$ \( T + 478 \) Copy content Toggle raw display
$67$ \( T + 334 \) Copy content Toggle raw display
$71$ \( T - 1062 \) Copy content Toggle raw display
$73$ \( T - 212 \) Copy content Toggle raw display
$79$ \( T + 640 \) Copy content Toggle raw display
$83$ \( T - 972 \) Copy content Toggle raw display
$89$ \( T - 120 \) Copy content Toggle raw display
$97$ \( T - 86 \) Copy content Toggle raw display
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