Properties

Label 1911.1.h.a
Level $1911$
Weight $1$
Character orbit 1911.h
Self dual yes
Analytic conductor $0.954$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -3, -39, 13
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1911.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.953713239142\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{-3}, \sqrt{13})\)
Artin image: $D_4$
Artin field: Galois closure of 4.0.5733.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - q^{4} + q^{9} + O(q^{10}) \) \( q + q^{3} - q^{4} + q^{9} - q^{12} + q^{13} + q^{16} - q^{25} + q^{27} - q^{36} + q^{39} + 2 q^{43} + q^{48} - q^{52} + 2 q^{61} - q^{64} - q^{75} - 2 q^{79} + q^{81} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times\).

\(n\) \(638\) \(1471\) \(1522\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1520.1
0
0 1.00000 −1.00000 0 0 0 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
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)
13.b even 2 1 RM by \(\Q(\sqrt{13}) \)
39.d odd 2 1 CM by \(\Q(\sqrt{-39}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1911.1.h.a 1
3.b odd 2 1 CM 1911.1.h.a 1
7.b odd 2 1 39.1.d.a 1
7.c even 3 2 1911.1.w.a 2
7.d odd 6 2 1911.1.w.b 2
13.b even 2 1 RM 1911.1.h.a 1
21.c even 2 1 39.1.d.a 1
21.g even 6 2 1911.1.w.b 2
21.h odd 6 2 1911.1.w.a 2
28.d even 2 1 624.1.l.a 1
35.c odd 2 1 975.1.g.a 1
35.f even 4 2 975.1.e.a 2
39.d odd 2 1 CM 1911.1.h.a 1
56.e even 2 1 2496.1.l.a 1
56.h odd 2 1 2496.1.l.b 1
63.l odd 6 2 1053.1.n.b 2
63.o even 6 2 1053.1.n.b 2
84.h odd 2 1 624.1.l.a 1
91.b odd 2 1 39.1.d.a 1
91.i even 4 2 507.1.c.a 1
91.n odd 6 2 507.1.h.a 2
91.r even 6 2 1911.1.w.a 2
91.s odd 6 2 1911.1.w.b 2
91.t odd 6 2 507.1.h.a 2
91.bc even 12 4 507.1.i.a 2
105.g even 2 1 975.1.g.a 1
105.k odd 4 2 975.1.e.a 2
168.e odd 2 1 2496.1.l.a 1
168.i even 2 1 2496.1.l.b 1
273.g even 2 1 39.1.d.a 1
273.o odd 4 2 507.1.c.a 1
273.u even 6 2 507.1.h.a 2
273.w odd 6 2 1911.1.w.a 2
273.ba even 6 2 1911.1.w.b 2
273.bn even 6 2 507.1.h.a 2
273.ca odd 12 4 507.1.i.a 2
364.h even 2 1 624.1.l.a 1
455.h odd 2 1 975.1.g.a 1
455.s even 4 2 975.1.e.a 2
728.b even 2 1 2496.1.l.a 1
728.l odd 2 1 2496.1.l.b 1
819.ce even 6 2 1053.1.n.b 2
819.cy odd 6 2 1053.1.n.b 2
1092.d odd 2 1 624.1.l.a 1
1365.g even 2 1 975.1.g.a 1
1365.bl odd 4 2 975.1.e.a 2
2184.y even 2 1 2496.1.l.b 1
2184.bf odd 2 1 2496.1.l.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
39.1.d.a 1 7.b odd 2 1
39.1.d.a 1 21.c even 2 1
39.1.d.a 1 91.b odd 2 1
39.1.d.a 1 273.g even 2 1
507.1.c.a 1 91.i even 4 2
507.1.c.a 1 273.o odd 4 2
507.1.h.a 2 91.n odd 6 2
507.1.h.a 2 91.t odd 6 2
507.1.h.a 2 273.u even 6 2
507.1.h.a 2 273.bn even 6 2
507.1.i.a 2 91.bc even 12 4
507.1.i.a 2 273.ca odd 12 4
624.1.l.a 1 28.d even 2 1
624.1.l.a 1 84.h odd 2 1
624.1.l.a 1 364.h even 2 1
624.1.l.a 1 1092.d odd 2 1
975.1.e.a 2 35.f even 4 2
975.1.e.a 2 105.k odd 4 2
975.1.e.a 2 455.s even 4 2
975.1.e.a 2 1365.bl odd 4 2
975.1.g.a 1 35.c odd 2 1
975.1.g.a 1 105.g even 2 1
975.1.g.a 1 455.h odd 2 1
975.1.g.a 1 1365.g even 2 1
1053.1.n.b 2 63.l odd 6 2
1053.1.n.b 2 63.o even 6 2
1053.1.n.b 2 819.ce even 6 2
1053.1.n.b 2 819.cy odd 6 2
1911.1.h.a 1 1.a even 1 1 trivial
1911.1.h.a 1 3.b odd 2 1 CM
1911.1.h.a 1 13.b even 2 1 RM
1911.1.h.a 1 39.d odd 2 1 CM
1911.1.w.a 2 7.c even 3 2
1911.1.w.a 2 21.h odd 6 2
1911.1.w.a 2 91.r even 6 2
1911.1.w.a 2 273.w odd 6 2
1911.1.w.b 2 7.d odd 6 2
1911.1.w.b 2 21.g even 6 2
1911.1.w.b 2 91.s odd 6 2
1911.1.w.b 2 273.ba even 6 2
2496.1.l.a 1 56.e even 2 1
2496.1.l.a 1 168.e odd 2 1
2496.1.l.a 1 728.b even 2 1
2496.1.l.a 1 2184.bf odd 2 1
2496.1.l.b 1 56.h odd 2 1
2496.1.l.b 1 168.i even 2 1
2496.1.l.b 1 728.l odd 2 1
2496.1.l.b 1 2184.y even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1911, [\chi])\):

\( T_{2} \)
\( T_{61} - 2 \)
\( T_{199} - 2 \)

Hecke characteristic polynomials

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