Properties

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

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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

\(f(q)\) \(=\) \( q - q^{3} + q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} + q^{7} + q^{9} + 4q^{11} + 2q^{13} + 2q^{17} - 2q^{19} - q^{21} - 6q^{23} - q^{27} + 6q^{29} + 6q^{31} - 4q^{33} - 4q^{37} - 2q^{39} - 4q^{43} + 4q^{47} + q^{49} - 2q^{51} - 2q^{53} + 2q^{57} + 4q^{59} - 2q^{61} + q^{63} - 12q^{67} + 6q^{69} - 8q^{71} + 14q^{73} + 4q^{77} + 16q^{79} + q^{81} + 16q^{83} - 6q^{87} + 16q^{89} + 2q^{91} - 6q^{93} - 14q^{97} + 4q^{99} + O(q^{100}) \)

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:

Atkin-Lehner signs

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

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 2100.2.a.i 1
3.b odd 2 1 6300.2.a.r 1
4.b odd 2 1 8400.2.a.bm 1
5.b even 2 1 2100.2.a.n 1
5.c odd 4 2 420.2.k.b 2
15.d odd 2 1 6300.2.a.b 1
15.e even 4 2 1260.2.k.a 2
20.d odd 2 1 8400.2.a.o 1
20.e even 4 2 1680.2.t.g 2
35.f even 4 2 2940.2.k.b 2
35.k even 12 4 2940.2.bb.f 4
35.l odd 12 4 2940.2.bb.a 4
60.l odd 4 2 5040.2.t.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
420.2.k.b 2 5.c odd 4 2
1260.2.k.a 2 15.e even 4 2
1680.2.t.g 2 20.e even 4 2
2100.2.a.i 1 1.a even 1 1 trivial
2100.2.a.n 1 5.b even 2 1
2940.2.k.b 2 35.f even 4 2
2940.2.bb.a 4 35.l odd 12 4
2940.2.bb.f 4 35.k even 12 4
5040.2.t.d 2 60.l odd 4 2
6300.2.a.b 1 15.d odd 2 1
6300.2.a.r 1 3.b odd 2 1
8400.2.a.o 1 20.d odd 2 1
8400.2.a.bm 1 4.b odd 2 1

Hecke kernels

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

\( T_{11} - 4 \)
\( T_{13} - 2 \)
\( T_{17} - 2 \)

Hecke characteristic polynomials

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