Properties

Label 2695.2.a.c
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 55)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} - 3q^{9} - q^{10} - q^{11} - 2q^{13} - q^{16} - 6q^{17} - 3q^{18} + 4q^{19} + q^{20} - q^{22} + 4q^{23} + q^{25} - 2q^{26} + 6q^{29} + 8q^{31} + 5q^{32} - 6q^{34} + 3q^{36} - 2q^{37} + 4q^{38} + 3q^{40} - 2q^{41} + 4q^{43} + q^{44} + 3q^{45} + 4q^{46} + 12q^{47} + q^{50} + 2q^{52} - 2q^{53} + q^{55} + 6q^{58} - 4q^{59} + 10q^{61} + 8q^{62} + 7q^{64} + 2q^{65} - 16q^{67} + 6q^{68} + 8q^{71} + 9q^{72} - 14q^{73} - 2q^{74} - 4q^{76} + 8q^{79} + q^{80} + 9q^{81} - 2q^{82} + 4q^{83} + 6q^{85} + 4q^{86} + 3q^{88} - 10q^{89} + 3q^{90} - 4q^{92} + 12q^{94} - 4q^{95} - 10q^{97} + 3q^{99} + O(q^{100}) \)

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
1.00000 0 −1.00000 −1.00000 0 0 −3.00000 −3.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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.c 1
7.b odd 2 1 55.2.a.a 1
21.c even 2 1 495.2.a.a 1
28.d even 2 1 880.2.a.h 1
35.c odd 2 1 275.2.a.a 1
35.f even 4 2 275.2.b.b 2
56.e even 2 1 3520.2.a.n 1
56.h odd 2 1 3520.2.a.p 1
77.b even 2 1 605.2.a.b 1
77.j odd 10 4 605.2.g.a 4
77.l even 10 4 605.2.g.c 4
84.h odd 2 1 7920.2.a.i 1
91.b odd 2 1 9295.2.a.b 1
105.g even 2 1 2475.2.a.i 1
105.k odd 4 2 2475.2.c.f 2
140.c even 2 1 4400.2.a.p 1
140.j odd 4 2 4400.2.b.n 2
231.h odd 2 1 5445.2.a.i 1
308.g odd 2 1 9680.2.a.r 1
385.h even 2 1 3025.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.2.a.a 1 7.b odd 2 1
275.2.a.a 1 35.c odd 2 1
275.2.b.b 2 35.f even 4 2
495.2.a.a 1 21.c even 2 1
605.2.a.b 1 77.b even 2 1
605.2.g.a 4 77.j odd 10 4
605.2.g.c 4 77.l even 10 4
880.2.a.h 1 28.d even 2 1
2475.2.a.i 1 105.g even 2 1
2475.2.c.f 2 105.k odd 4 2
2695.2.a.c 1 1.a even 1 1 trivial
3025.2.a.f 1 385.h even 2 1
3520.2.a.n 1 56.e even 2 1
3520.2.a.p 1 56.h odd 2 1
4400.2.a.p 1 140.c even 2 1
4400.2.b.n 2 140.j odd 4 2
5445.2.a.i 1 231.h odd 2 1
7920.2.a.i 1 84.h odd 2 1
9295.2.a.b 1 91.b odd 2 1
9680.2.a.r 1 308.g odd 2 1

Atkin-Lehner signs

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

Hecke kernels

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

\( T_{2} - 1 \)
\( T_{3} \)

Hecke characteristic polynomials

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