Properties

Label 17.4.a.a
Level $17$
Weight $4$
Character orbit 17.a
Self dual yes
Analytic conductor $1.003$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.00303247010\)
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

\(f(q)\) \(=\) \( q - 3 q^{2} - 8 q^{3} + q^{4} + 6 q^{5} + 24 q^{6} - 28 q^{7} + 21 q^{8} + 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 3 q^{2} - 8 q^{3} + q^{4} + 6 q^{5} + 24 q^{6} - 28 q^{7} + 21 q^{8} + 37 q^{9} - 18 q^{10} - 24 q^{11} - 8 q^{12} - 58 q^{13} + 84 q^{14} - 48 q^{15} - 71 q^{16} + 17 q^{17} - 111 q^{18} + 116 q^{19} + 6 q^{20} + 224 q^{21} + 72 q^{22} - 60 q^{23} - 168 q^{24} - 89 q^{25} + 174 q^{26} - 80 q^{27} - 28 q^{28} + 30 q^{29} + 144 q^{30} - 172 q^{31} + 45 q^{32} + 192 q^{33} - 51 q^{34} - 168 q^{35} + 37 q^{36} - 58 q^{37} - 348 q^{38} + 464 q^{39} + 126 q^{40} - 342 q^{41} - 672 q^{42} - 148 q^{43} - 24 q^{44} + 222 q^{45} + 180 q^{46} + 288 q^{47} + 568 q^{48} + 441 q^{49} + 267 q^{50} - 136 q^{51} - 58 q^{52} + 318 q^{53} + 240 q^{54} - 144 q^{55} - 588 q^{56} - 928 q^{57} - 90 q^{58} + 252 q^{59} - 48 q^{60} + 110 q^{61} + 516 q^{62} - 1036 q^{63} + 433 q^{64} - 348 q^{65} - 576 q^{66} - 484 q^{67} + 17 q^{68} + 480 q^{69} + 504 q^{70} - 708 q^{71} + 777 q^{72} + 362 q^{73} + 174 q^{74} + 712 q^{75} + 116 q^{76} + 672 q^{77} - 1392 q^{78} - 484 q^{79} - 426 q^{80} - 359 q^{81} + 1026 q^{82} + 756 q^{83} + 224 q^{84} + 102 q^{85} + 444 q^{86} - 240 q^{87} - 504 q^{88} - 774 q^{89} - 666 q^{90} + 1624 q^{91} - 60 q^{92} + 1376 q^{93} - 864 q^{94} + 696 q^{95} - 360 q^{96} - 382 q^{97} - 1323 q^{98} - 888 q^{99}+O(q^{100}) \) 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
−3.00000 −8.00000 1.00000 6.00000 24.0000 −28.0000 21.0000 37.0000 −18.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(17\) \(-1\)

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 17.4.a.a 1
3.b odd 2 1 153.4.a.d 1
4.b odd 2 1 272.4.a.d 1
5.b even 2 1 425.4.a.d 1
5.c odd 4 2 425.4.b.c 2
7.b odd 2 1 833.4.a.a 1
8.b even 2 1 1088.4.a.l 1
8.d odd 2 1 1088.4.a.a 1
11.b odd 2 1 2057.4.a.d 1
12.b even 2 1 2448.4.a.f 1
17.b even 2 1 289.4.a.a 1
17.c even 4 2 289.4.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
17.4.a.a 1 1.a even 1 1 trivial
153.4.a.d 1 3.b odd 2 1
272.4.a.d 1 4.b odd 2 1
289.4.a.a 1 17.b even 2 1
289.4.b.a 2 17.c even 4 2
425.4.a.d 1 5.b even 2 1
425.4.b.c 2 5.c odd 4 2
833.4.a.a 1 7.b odd 2 1
1088.4.a.a 1 8.d odd 2 1
1088.4.a.l 1 8.b even 2 1
2057.4.a.d 1 11.b odd 2 1
2448.4.a.f 1 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 3 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 3 \) Copy content Toggle raw display
$3$ \( T + 8 \) Copy content Toggle raw display
$5$ \( T - 6 \) Copy content Toggle raw display
$7$ \( T + 28 \) Copy content Toggle raw display
$11$ \( T + 24 \) Copy content Toggle raw display
$13$ \( T + 58 \) Copy content Toggle raw display
$17$ \( T - 17 \) Copy content Toggle raw display
$19$ \( T - 116 \) Copy content Toggle raw display
$23$ \( T + 60 \) Copy content Toggle raw display
$29$ \( T - 30 \) Copy content Toggle raw display
$31$ \( T + 172 \) Copy content Toggle raw display
$37$ \( T + 58 \) Copy content Toggle raw display
$41$ \( T + 342 \) Copy content Toggle raw display
$43$ \( T + 148 \) Copy content Toggle raw display
$47$ \( T - 288 \) Copy content Toggle raw display
$53$ \( T - 318 \) Copy content Toggle raw display
$59$ \( T - 252 \) Copy content Toggle raw display
$61$ \( T - 110 \) Copy content Toggle raw display
$67$ \( T + 484 \) Copy content Toggle raw display
$71$ \( T + 708 \) Copy content Toggle raw display
$73$ \( T - 362 \) Copy content Toggle raw display
$79$ \( T + 484 \) Copy content Toggle raw display
$83$ \( T - 756 \) Copy content Toggle raw display
$89$ \( T + 774 \) Copy content Toggle raw display
$97$ \( T + 382 \) Copy content Toggle raw display
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