Properties

Label 98.4.a.c
Level $98$
Weight $4$
Character orbit 98.a
Self dual yes
Analytic conductor $5.782$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.78218718056\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{2} + q^{3} + 4 q^{4} - 7 q^{5} - 2 q^{6} - 8 q^{8} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + q^{3} + 4 q^{4} - 7 q^{5} - 2 q^{6} - 8 q^{8} - 26 q^{9} + 14 q^{10} + 35 q^{11} + 4 q^{12} - 66 q^{13} - 7 q^{15} + 16 q^{16} - 59 q^{17} + 52 q^{18} - 137 q^{19} - 28 q^{20} - 70 q^{22} - 7 q^{23} - 8 q^{24} - 76 q^{25} + 132 q^{26} - 53 q^{27} + 106 q^{29} + 14 q^{30} - 75 q^{31} - 32 q^{32} + 35 q^{33} + 118 q^{34} - 104 q^{36} + 11 q^{37} + 274 q^{38} - 66 q^{39} + 56 q^{40} + 498 q^{41} + 260 q^{43} + 140 q^{44} + 182 q^{45} + 14 q^{46} + 171 q^{47} + 16 q^{48} + 152 q^{50} - 59 q^{51} - 264 q^{52} - 417 q^{53} + 106 q^{54} - 245 q^{55} - 137 q^{57} - 212 q^{58} + 17 q^{59} - 28 q^{60} - 51 q^{61} + 150 q^{62} + 64 q^{64} + 462 q^{65} - 70 q^{66} + 439 q^{67} - 236 q^{68} - 7 q^{69} - 784 q^{71} + 208 q^{72} - 295 q^{73} - 22 q^{74} - 76 q^{75} - 548 q^{76} + 132 q^{78} - 495 q^{79} - 112 q^{80} + 649 q^{81} - 996 q^{82} - 932 q^{83} + 413 q^{85} - 520 q^{86} + 106 q^{87} - 280 q^{88} + 873 q^{89} - 364 q^{90} - 28 q^{92} - 75 q^{93} - 342 q^{94} + 959 q^{95} - 32 q^{96} + 290 q^{97} - 910 q^{99}+O(q^{100}) \) 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 1.00000 4.00000 −7.00000 −2.00000 0 −8.00000 −26.0000 14.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 98.4.a.c 1
3.b odd 2 1 882.4.a.p 1
4.b odd 2 1 784.4.a.j 1
5.b even 2 1 2450.4.a.bf 1
7.b odd 2 1 98.4.a.b 1
7.c even 3 2 98.4.c.e 2
7.d odd 6 2 14.4.c.b 2
21.c even 2 1 882.4.a.k 1
21.g even 6 2 126.4.g.c 2
21.h odd 6 2 882.4.g.d 2
28.d even 2 1 784.4.a.l 1
28.f even 6 2 112.4.i.b 2
35.c odd 2 1 2450.4.a.bh 1
35.i odd 6 2 350.4.e.b 2
35.k even 12 4 350.4.j.d 4
56.j odd 6 2 448.4.i.c 2
56.m even 6 2 448.4.i.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.c.b 2 7.d odd 6 2
98.4.a.b 1 7.b odd 2 1
98.4.a.c 1 1.a even 1 1 trivial
98.4.c.e 2 7.c even 3 2
112.4.i.b 2 28.f even 6 2
126.4.g.c 2 21.g even 6 2
350.4.e.b 2 35.i odd 6 2
350.4.j.d 4 35.k even 12 4
448.4.i.c 2 56.j odd 6 2
448.4.i.d 2 56.m even 6 2
784.4.a.j 1 4.b odd 2 1
784.4.a.l 1 28.d even 2 1
882.4.a.k 1 21.c even 2 1
882.4.a.p 1 3.b odd 2 1
882.4.g.d 2 21.h odd 6 2
2450.4.a.bf 1 5.b even 2 1
2450.4.a.bh 1 35.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(98))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T + 7 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 35 \) Copy content Toggle raw display
$13$ \( T + 66 \) Copy content Toggle raw display
$17$ \( T + 59 \) Copy content Toggle raw display
$19$ \( T + 137 \) Copy content Toggle raw display
$23$ \( T + 7 \) Copy content Toggle raw display
$29$ \( T - 106 \) Copy content Toggle raw display
$31$ \( T + 75 \) Copy content Toggle raw display
$37$ \( T - 11 \) Copy content Toggle raw display
$41$ \( T - 498 \) Copy content Toggle raw display
$43$ \( T - 260 \) Copy content Toggle raw display
$47$ \( T - 171 \) Copy content Toggle raw display
$53$ \( T + 417 \) Copy content Toggle raw display
$59$ \( T - 17 \) Copy content Toggle raw display
$61$ \( T + 51 \) Copy content Toggle raw display
$67$ \( T - 439 \) Copy content Toggle raw display
$71$ \( T + 784 \) Copy content Toggle raw display
$73$ \( T + 295 \) Copy content Toggle raw display
$79$ \( T + 495 \) Copy content Toggle raw display
$83$ \( T + 932 \) Copy content Toggle raw display
$89$ \( T - 873 \) Copy content Toggle raw display
$97$ \( T - 290 \) Copy content Toggle raw display
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