Properties

Label 105.2.a.a
Level $105$
Weight $2$
Character orbit 105.a
Self dual yes
Analytic conductor $0.838$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.838429221223\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + q^{10} - q^{12} - 6q^{13} + q^{14} + q^{15} - q^{16} + 2q^{17} + q^{18} - 8q^{19} - q^{20} + q^{21} + 8q^{23} - 3q^{24} + q^{25} - 6q^{26} + q^{27} - q^{28} - 2q^{29} + q^{30} + 4q^{31} + 5q^{32} + 2q^{34} + q^{35} - q^{36} - 2q^{37} - 8q^{38} - 6q^{39} - 3q^{40} - 6q^{41} + q^{42} + 4q^{43} + q^{45} + 8q^{46} + 8q^{47} - q^{48} + q^{49} + q^{50} + 2q^{51} + 6q^{52} + 10q^{53} + q^{54} - 3q^{56} - 8q^{57} - 2q^{58} + 4q^{59} - q^{60} - 2q^{61} + 4q^{62} + q^{63} + 7q^{64} - 6q^{65} + 4q^{67} - 2q^{68} + 8q^{69} + q^{70} - 12q^{71} - 3q^{72} - 2q^{73} - 2q^{74} + q^{75} + 8q^{76} - 6q^{78} + 8q^{79} - q^{80} + q^{81} - 6q^{82} - 4q^{83} - q^{84} + 2q^{85} + 4q^{86} - 2q^{87} - 6q^{89} + q^{90} - 6q^{91} - 8q^{92} + 4q^{93} + 8q^{94} - 8q^{95} + 5q^{96} - 18q^{97} + q^{98} + O(q^{100}) \)

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
1.00000 1.00000 −1.00000 1.00000 1.00000 1.00000 −3.00000 1.00000 1.00000
\(n\): 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 105.2.a.a 1
3.b odd 2 1 315.2.a.a 1
4.b odd 2 1 1680.2.a.f 1
5.b even 2 1 525.2.a.a 1
5.c odd 4 2 525.2.d.b 2
7.b odd 2 1 735.2.a.f 1
7.c even 3 2 735.2.i.a 2
7.d odd 6 2 735.2.i.b 2
8.b even 2 1 6720.2.a.p 1
8.d odd 2 1 6720.2.a.bk 1
12.b even 2 1 5040.2.a.d 1
15.d odd 2 1 1575.2.a.h 1
15.e even 4 2 1575.2.d.b 2
20.d odd 2 1 8400.2.a.co 1
21.c even 2 1 2205.2.a.b 1
35.c odd 2 1 3675.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.2.a.a 1 1.a even 1 1 trivial
315.2.a.a 1 3.b odd 2 1
525.2.a.a 1 5.b even 2 1
525.2.d.b 2 5.c odd 4 2
735.2.a.f 1 7.b odd 2 1
735.2.i.a 2 7.c even 3 2
735.2.i.b 2 7.d odd 6 2
1575.2.a.h 1 15.d odd 2 1
1575.2.d.b 2 15.e even 4 2
1680.2.a.f 1 4.b odd 2 1
2205.2.a.b 1 21.c even 2 1
3675.2.a.f 1 35.c odd 2 1
5040.2.a.d 1 12.b even 2 1
6720.2.a.p 1 8.b even 2 1
6720.2.a.bk 1 8.d odd 2 1
8400.2.a.co 1 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(105))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( T \)
$13$ \( 6 + T \)
$17$ \( -2 + T \)
$19$ \( 8 + T \)
$23$ \( -8 + T \)
$29$ \( 2 + T \)
$31$ \( -4 + T \)
$37$ \( 2 + T \)
$41$ \( 6 + T \)
$43$ \( -4 + T \)
$47$ \( -8 + T \)
$53$ \( -10 + T \)
$59$ \( -4 + T \)
$61$ \( 2 + T \)
$67$ \( -4 + T \)
$71$ \( 12 + T \)
$73$ \( 2 + T \)
$79$ \( -8 + T \)
$83$ \( 4 + T \)
$89$ \( 6 + T \)
$97$ \( 18 + T \)
show more
show less