Properties

Label 2100.2.a.d
Level 2100
Weight 2
Character orbit 2100.a
Self dual yes
Analytic conductor 16.769
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 420)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - q^{7} + q^{9} + 6q^{11} + 4q^{13} - 6q^{17} + 2q^{19} + q^{21} - q^{27} + 6q^{29} - 10q^{31} - 6q^{33} - 2q^{37} - 4q^{39} - 6q^{41} + 4q^{43} + q^{49} + 6q^{51} + 12q^{53} - 2q^{57} + 14q^{61} - q^{63} + 4q^{67} + 6q^{71} + 4q^{73} - 6q^{77} - 16q^{79} + q^{81} + 12q^{83} - 6q^{87} + 6q^{89} - 4q^{91} + 10q^{93} + 16q^{97} + 6q^{99} + O(q^{100}) \)

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
0 −1.00000 0 0 0 −1.00000 0 1.00000 0
\(n\): 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 2100.2.a.d 1
3.b odd 2 1 6300.2.a.a 1
4.b odd 2 1 8400.2.a.cj 1
5.b even 2 1 420.2.a.c 1
5.c odd 4 2 2100.2.k.j 2
15.d odd 2 1 1260.2.a.i 1
15.e even 4 2 6300.2.k.a 2
20.d odd 2 1 1680.2.a.a 1
35.c odd 2 1 2940.2.a.f 1
35.i odd 6 2 2940.2.q.i 2
35.j even 6 2 2940.2.q.e 2
40.e odd 2 1 6720.2.a.ch 1
40.f even 2 1 6720.2.a.x 1
60.h even 2 1 5040.2.a.bc 1
105.g even 2 1 8820.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
420.2.a.c 1 5.b even 2 1
1260.2.a.i 1 15.d odd 2 1
1680.2.a.a 1 20.d odd 2 1
2100.2.a.d 1 1.a even 1 1 trivial
2100.2.k.j 2 5.c odd 4 2
2940.2.a.f 1 35.c odd 2 1
2940.2.q.e 2 35.j even 6 2
2940.2.q.i 2 35.i odd 6 2
5040.2.a.bc 1 60.h even 2 1
6300.2.a.a 1 3.b odd 2 1
6300.2.k.a 2 15.e even 4 2
6720.2.a.x 1 40.f even 2 1
6720.2.a.ch 1 40.e odd 2 1
8400.2.a.cj 1 4.b odd 2 1
8820.2.a.b 1 105.g even 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(1\)
\(7\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2100))\):

\( T_{11} - 6 \)
\( T_{13} - 4 \)
\( T_{17} + 6 \)

Hecke characteristic polynomials

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