Properties

Label 2695.2.a.b
Level $2695$
Weight $2$
Character orbit 2695.a
Self dual yes
Analytic conductor $21.520$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.5196833447\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 385)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 3 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 3 q^{8} + q^{9} + q^{10} - q^{11} - 2 q^{12} - 4 q^{13} - 2 q^{15} - q^{16} + 4 q^{17} - q^{18} + 8 q^{19} + q^{20} + q^{22} + 6 q^{24} + q^{25} + 4 q^{26} - 4 q^{27} - 6 q^{29} + 2 q^{30} + 6 q^{31} - 5 q^{32} - 2 q^{33} - 4 q^{34} - q^{36} - 6 q^{37} - 8 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{43} + q^{44} - q^{45} + 6 q^{47} - 2 q^{48} - q^{50} + 8 q^{51} + 4 q^{52} + 10 q^{53} + 4 q^{54} + q^{55} + 16 q^{57} + 6 q^{58} + 14 q^{59} + 2 q^{60} - 12 q^{61} - 6 q^{62} + 7 q^{64} + 4 q^{65} + 2 q^{66} + 12 q^{67} - 4 q^{68} - 12 q^{71} + 3 q^{72} + 8 q^{73} + 6 q^{74} + 2 q^{75} - 8 q^{76} + 8 q^{78} + 8 q^{79} + q^{80} - 11 q^{81} + 16 q^{83} - 4 q^{85} + 4 q^{86} - 12 q^{87} - 3 q^{88} + 14 q^{89} + q^{90} + 12 q^{93} - 6 q^{94} - 8 q^{95} - 10 q^{96} + 2 q^{97} - q^{99}+O(q^{100}) \) 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
−1.00000 2.00000 −1.00000 −1.00000 −2.00000 0 3.00000 1.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)
\(11\) \(1\)

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 2695.2.a.b 1
7.b odd 2 1 385.2.a.a 1
21.c even 2 1 3465.2.a.p 1
28.d even 2 1 6160.2.a.o 1
35.c odd 2 1 1925.2.a.j 1
35.f even 4 2 1925.2.b.c 2
77.b even 2 1 4235.2.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
385.2.a.a 1 7.b odd 2 1
1925.2.a.j 1 35.c odd 2 1
1925.2.b.c 2 35.f even 4 2
2695.2.a.b 1 1.a even 1 1 trivial
3465.2.a.p 1 21.c even 2 1
4235.2.a.e 1 77.b even 2 1
6160.2.a.o 1 28.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2695))\):

\( T_{2} + 1 \) Copy content Toggle raw display
\( T_{3} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T - 2 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 1 \) Copy content Toggle raw display
$13$ \( T + 4 \) Copy content Toggle raw display
$17$ \( T - 4 \) Copy content Toggle raw display
$19$ \( T - 8 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T - 6 \) Copy content Toggle raw display
$37$ \( T + 6 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T - 6 \) Copy content Toggle raw display
$53$ \( T - 10 \) Copy content Toggle raw display
$59$ \( T - 14 \) Copy content Toggle raw display
$61$ \( T + 12 \) Copy content Toggle raw display
$67$ \( T - 12 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T - 8 \) Copy content Toggle raw display
$79$ \( T - 8 \) Copy content Toggle raw display
$83$ \( T - 16 \) Copy content Toggle raw display
$89$ \( T - 14 \) Copy content Toggle raw display
$97$ \( T - 2 \) Copy content Toggle raw display
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