Properties

Label 2100.4.a.g
Level $2100$
Weight $4$
Character orbit 2100.a
Self dual yes
Analytic conductor $123.904$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2100.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(123.904011012\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 3q^{3} + 7q^{7} + 9q^{9} + O(q^{10}) \) \( q - 3q^{3} + 7q^{7} + 9q^{9} + 4q^{11} - 54q^{13} + 14q^{17} + 92q^{19} - 21q^{21} + 152q^{23} - 27q^{27} - 106q^{29} - 144q^{31} - 12q^{33} - 158q^{37} + 162q^{39} - 390q^{41} + 508q^{43} + 528q^{47} + 49q^{49} - 42q^{51} - 606q^{53} - 276q^{57} - 364q^{59} + 678q^{61} + 63q^{63} - 844q^{67} - 456q^{69} - 8q^{71} + 422q^{73} + 28q^{77} + 384q^{79} + 81q^{81} + 548q^{83} + 318q^{87} + 1194q^{89} - 378q^{91} + 432q^{93} + 1502q^{97} + 36q^{99} + O(q^{100}) \)

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 −3.00000 0 0 0 7.00000 0 9.00000 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 2100.4.a.g 1
5.b even 2 1 84.4.a.b 1
5.c odd 4 2 2100.4.k.g 2
15.d odd 2 1 252.4.a.a 1
20.d odd 2 1 336.4.a.e 1
35.c odd 2 1 588.4.a.a 1
35.i odd 6 2 588.4.i.h 2
35.j even 6 2 588.4.i.a 2
40.e odd 2 1 1344.4.a.p 1
40.f even 2 1 1344.4.a.b 1
60.h even 2 1 1008.4.a.d 1
105.g even 2 1 1764.4.a.l 1
105.o odd 6 2 1764.4.k.n 2
105.p even 6 2 1764.4.k.c 2
140.c even 2 1 2352.4.a.v 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
84.4.a.b 1 5.b even 2 1
252.4.a.a 1 15.d odd 2 1
336.4.a.e 1 20.d odd 2 1
588.4.a.a 1 35.c odd 2 1
588.4.i.a 2 35.j even 6 2
588.4.i.h 2 35.i odd 6 2
1008.4.a.d 1 60.h even 2 1
1344.4.a.b 1 40.f even 2 1
1344.4.a.p 1 40.e odd 2 1
1764.4.a.l 1 105.g even 2 1
1764.4.k.c 2 105.p even 6 2
1764.4.k.n 2 105.o odd 6 2
2100.4.a.g 1 1.a even 1 1 trivial
2100.4.k.g 2 5.c odd 4 2
2352.4.a.v 1 140.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2100))\):

\( T_{11} - 4 \)
\( T_{13} + 54 \)
\( T_{17} - 14 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 3 + T \)
$5$ \( T \)
$7$ \( -7 + T \)
$11$ \( -4 + T \)
$13$ \( 54 + T \)
$17$ \( -14 + T \)
$19$ \( -92 + T \)
$23$ \( -152 + T \)
$29$ \( 106 + T \)
$31$ \( 144 + T \)
$37$ \( 158 + T \)
$41$ \( 390 + T \)
$43$ \( -508 + T \)
$47$ \( -528 + T \)
$53$ \( 606 + T \)
$59$ \( 364 + T \)
$61$ \( -678 + T \)
$67$ \( 844 + T \)
$71$ \( 8 + T \)
$73$ \( -422 + T \)
$79$ \( -384 + T \)
$83$ \( -548 + T \)
$89$ \( -1194 + T \)
$97$ \( -1502 + T \)
show more
show less