Properties

Label 1900.1.e.a
Level $1900$
Weight $1$
Character orbit 1900.e
Self dual yes
Analytic conductor $0.948$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -19
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1900.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.948223524003\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 76)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.76.1
Artin image $D_6$
Artin field Galois closure of 6.2.722000.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{7} + q^{9} + O(q^{10}) \) \( q + q^{7} + q^{9} - q^{11} + q^{17} + q^{19} - 2q^{23} + q^{43} + q^{47} - q^{61} + q^{63} + q^{73} - q^{77} + q^{81} - 2q^{83} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1101.1
0
0 0 0 0 0 1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.b odd 2 1 CM by \(\Q(\sqrt{-19}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1900.1.e.a 1
5.b even 2 1 76.1.c.a 1
5.c odd 4 2 1900.1.g.a 2
15.d odd 2 1 684.1.h.a 1
19.b odd 2 1 CM 1900.1.e.a 1
20.d odd 2 1 304.1.e.a 1
35.c odd 2 1 3724.1.e.c 1
35.i odd 6 2 3724.1.bc.b 2
35.j even 6 2 3724.1.bc.c 2
40.e odd 2 1 1216.1.e.b 1
40.f even 2 1 1216.1.e.a 1
60.h even 2 1 2736.1.o.b 1
95.d odd 2 1 76.1.c.a 1
95.g even 4 2 1900.1.g.a 2
95.h odd 6 2 1444.1.h.a 2
95.i even 6 2 1444.1.h.a 2
95.o odd 18 6 1444.1.j.a 6
95.p even 18 6 1444.1.j.a 6
285.b even 2 1 684.1.h.a 1
380.d even 2 1 304.1.e.a 1
665.g even 2 1 3724.1.e.c 1
665.x odd 6 2 3724.1.bc.c 2
665.y even 6 2 3724.1.bc.b 2
760.b odd 2 1 1216.1.e.a 1
760.p even 2 1 1216.1.e.b 1
1140.p odd 2 1 2736.1.o.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
76.1.c.a 1 5.b even 2 1
76.1.c.a 1 95.d odd 2 1
304.1.e.a 1 20.d odd 2 1
304.1.e.a 1 380.d even 2 1
684.1.h.a 1 15.d odd 2 1
684.1.h.a 1 285.b even 2 1
1216.1.e.a 1 40.f even 2 1
1216.1.e.a 1 760.b odd 2 1
1216.1.e.b 1 40.e odd 2 1
1216.1.e.b 1 760.p even 2 1
1444.1.h.a 2 95.h odd 6 2
1444.1.h.a 2 95.i even 6 2
1444.1.j.a 6 95.o odd 18 6
1444.1.j.a 6 95.p even 18 6
1900.1.e.a 1 1.a even 1 1 trivial
1900.1.e.a 1 19.b odd 2 1 CM
1900.1.g.a 2 5.c odd 4 2
1900.1.g.a 2 95.g even 4 2
2736.1.o.b 1 60.h even 2 1
2736.1.o.b 1 1140.p odd 2 1
3724.1.e.c 1 35.c odd 2 1
3724.1.e.c 1 665.g even 2 1
3724.1.bc.b 2 35.i odd 6 2
3724.1.bc.b 2 665.y even 6 2
3724.1.bc.c 2 35.j even 6 2
3724.1.bc.c 2 665.x odd 6 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} - 1 \) acting on \(S_{1}^{\mathrm{new}}(1900, [\chi])\).

Hecke characteristic polynomials

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