Properties

Label 105.4.a.b
Level $105$
Weight $4$
Character orbit 105.a
Self dual yes
Analytic conductor $6.195$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 5q^{2} - 3q^{3} + 17q^{4} + 5q^{5} - 15q^{6} + 7q^{7} + 45q^{8} + 9q^{9} + O(q^{10}) \) \( q + 5q^{2} - 3q^{3} + 17q^{4} + 5q^{5} - 15q^{6} + 7q^{7} + 45q^{8} + 9q^{9} + 25q^{10} + 12q^{11} - 51q^{12} + 30q^{13} + 35q^{14} - 15q^{15} + 89q^{16} - 134q^{17} + 45q^{18} - 92q^{19} + 85q^{20} - 21q^{21} + 60q^{22} + 112q^{23} - 135q^{24} + 25q^{25} + 150q^{26} - 27q^{27} + 119q^{28} - 58q^{29} - 75q^{30} - 224q^{31} + 85q^{32} - 36q^{33} - 670q^{34} + 35q^{35} + 153q^{36} - 146q^{37} - 460q^{38} - 90q^{39} + 225q^{40} + 18q^{41} - 105q^{42} + 340q^{43} + 204q^{44} + 45q^{45} + 560q^{46} + 208q^{47} - 267q^{48} + 49q^{49} + 125q^{50} + 402q^{51} + 510q^{52} - 754q^{53} - 135q^{54} + 60q^{55} + 315q^{56} + 276q^{57} - 290q^{58} + 380q^{59} - 255q^{60} + 718q^{61} - 1120q^{62} + 63q^{63} - 287q^{64} + 150q^{65} - 180q^{66} + 412q^{67} - 2278q^{68} - 336q^{69} + 175q^{70} - 960q^{71} + 405q^{72} + 1066q^{73} - 730q^{74} - 75q^{75} - 1564q^{76} + 84q^{77} - 450q^{78} + 896q^{79} + 445q^{80} + 81q^{81} + 90q^{82} + 436q^{83} - 357q^{84} - 670q^{85} + 1700q^{86} + 174q^{87} + 540q^{88} - 1038q^{89} + 225q^{90} + 210q^{91} + 1904q^{92} + 672q^{93} + 1040q^{94} - 460q^{95} - 255q^{96} - 702q^{97} + 245q^{98} + 108q^{99} + O(q^{100}) \)

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
5.00000 −3.00000 17.0000 5.00000 −15.0000 7.00000 45.0000 9.00000 25.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(5\) \(-1\)
\(7\) \(-1\)

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 105.4.a.b 1
3.b odd 2 1 315.4.a.a 1
4.b odd 2 1 1680.4.a.u 1
5.b even 2 1 525.4.a.a 1
5.c odd 4 2 525.4.d.a 2
7.b odd 2 1 735.4.a.j 1
15.d odd 2 1 1575.4.a.l 1
21.c even 2 1 2205.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.4.a.b 1 1.a even 1 1 trivial
315.4.a.a 1 3.b odd 2 1
525.4.a.a 1 5.b even 2 1
525.4.d.a 2 5.c odd 4 2
735.4.a.j 1 7.b odd 2 1
1575.4.a.l 1 15.d odd 2 1
1680.4.a.u 1 4.b odd 2 1
2205.4.a.b 1 21.c even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 5 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(105))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -5 + T \)
$3$ \( 3 + T \)
$5$ \( -5 + T \)
$7$ \( -7 + T \)
$11$ \( -12 + T \)
$13$ \( -30 + T \)
$17$ \( 134 + T \)
$19$ \( 92 + T \)
$23$ \( -112 + T \)
$29$ \( 58 + T \)
$31$ \( 224 + T \)
$37$ \( 146 + T \)
$41$ \( -18 + T \)
$43$ \( -340 + T \)
$47$ \( -208 + T \)
$53$ \( 754 + T \)
$59$ \( -380 + T \)
$61$ \( -718 + T \)
$67$ \( -412 + T \)
$71$ \( 960 + T \)
$73$ \( -1066 + T \)
$79$ \( -896 + T \)
$83$ \( -436 + T \)
$89$ \( 1038 + T \)
$97$ \( 702 + T \)
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