Properties

Label 1805.1.o.a
Level $1805$
Weight $1$
Character orbit 1805.o
Analytic conductor $0.901$
Analytic rank $0$
Dimension $6$
Projective image $D_{2}$
CM/RM discs -19, -95, 5
Inner twists $24$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1805.o (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.900812347803\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{5}, \sqrt{-19})\)
Artin image: $C_9\times D_4$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{36} - \cdots)\)

$q$-expansion

The \(q\)-expansion and trace form are shown below.

\(f(q)\) \(=\) \( q - \zeta_{18}^{2} q^{4} - \zeta_{18}^{7} q^{5} - \zeta_{18}^{8} q^{9} +O(q^{10}) \) Copy content Toggle raw display \( q - \zeta_{18}^{2} q^{4} - \zeta_{18}^{7} q^{5} - \zeta_{18}^{8} q^{9} + \zeta_{18}^{3} q^{11} + \zeta_{18}^{4} q^{16} - q^{20} - \zeta_{18}^{5} q^{25} - \zeta_{18} q^{36} - 2 \zeta_{18}^{5} q^{44} - \zeta_{18}^{6} q^{45} - \zeta_{18}^{3} q^{49} + 2 \zeta_{18} q^{55} - \zeta_{18}^{2} q^{61} - \zeta_{18}^{6} q^{64} + \zeta_{18}^{2} q^{80} - \zeta_{18}^{7} q^{81} + 2 \zeta_{18}^{2} q^{99} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{11} - 6 q^{20} + 3 q^{45} - 3 q^{49} + 3 q^{64}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(-\zeta_{18}^{2}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
299.1
0.939693 0.342020i
−0.173648 0.984808i
−0.766044 + 0.642788i
0.939693 + 0.342020i
−0.766044 0.642788i
−0.173648 + 0.984808i
0 0 −0.766044 + 0.642788i 0.766044 + 0.642788i 0 0 0 0.939693 + 0.342020i 0
694.1 0 0 0.939693 0.342020i −0.939693 0.342020i 0 0 0 −0.173648 + 0.984808i 0
849.1 0 0 −0.173648 + 0.984808i 0.173648 + 0.984808i 0 0 0 −0.766044 0.642788i 0
984.1 0 0 −0.766044 0.642788i 0.766044 0.642788i 0 0 0 0.939693 0.342020i 0
1029.1 0 0 −0.173648 0.984808i 0.173648 0.984808i 0 0 0 −0.766044 + 0.642788i 0
1199.1 0 0 0.939693 + 0.342020i −0.939693 + 0.342020i 0 0 0 −0.173648 0.984808i 0
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1199.1
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 RM by \(\Q(\sqrt{5}) \)
19.b odd 2 1 CM by \(\Q(\sqrt{-19}) \)
95.d odd 2 1 CM by \(\Q(\sqrt{-95}) \)
19.c even 3 2 inner
19.d odd 6 2 inner
19.e even 9 3 inner
19.f odd 18 3 inner
95.h odd 6 2 inner
95.i even 6 2 inner
95.o odd 18 3 inner
95.p even 18 3 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1805.1.o.a 6
5.b even 2 1 RM 1805.1.o.a 6
19.b odd 2 1 CM 1805.1.o.a 6
19.c even 3 2 inner 1805.1.o.a 6
19.d odd 6 2 inner 1805.1.o.a 6
19.e even 9 1 95.1.d.a 1
19.e even 9 2 1805.1.h.a 2
19.e even 9 3 inner 1805.1.o.a 6
19.f odd 18 1 95.1.d.a 1
19.f odd 18 2 1805.1.h.a 2
19.f odd 18 3 inner 1805.1.o.a 6
57.j even 18 1 855.1.g.a 1
57.l odd 18 1 855.1.g.a 1
76.k even 18 1 1520.1.m.a 1
76.l odd 18 1 1520.1.m.a 1
95.d odd 2 1 CM 1805.1.o.a 6
95.h odd 6 2 inner 1805.1.o.a 6
95.i even 6 2 inner 1805.1.o.a 6
95.o odd 18 1 95.1.d.a 1
95.o odd 18 2 1805.1.h.a 2
95.o odd 18 3 inner 1805.1.o.a 6
95.p even 18 1 95.1.d.a 1
95.p even 18 2 1805.1.h.a 2
95.p even 18 3 inner 1805.1.o.a 6
95.q odd 36 2 475.1.c.a 1
95.r even 36 2 475.1.c.a 1
285.bd odd 18 1 855.1.g.a 1
285.bf even 18 1 855.1.g.a 1
380.ba odd 18 1 1520.1.m.a 1
380.bb even 18 1 1520.1.m.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.1.d.a 1 19.e even 9 1
95.1.d.a 1 19.f odd 18 1
95.1.d.a 1 95.o odd 18 1
95.1.d.a 1 95.p even 18 1
475.1.c.a 1 95.q odd 36 2
475.1.c.a 1 95.r even 36 2
855.1.g.a 1 57.j even 18 1
855.1.g.a 1 57.l odd 18 1
855.1.g.a 1 285.bd odd 18 1
855.1.g.a 1 285.bf even 18 1
1520.1.m.a 1 76.k even 18 1
1520.1.m.a 1 76.l odd 18 1
1520.1.m.a 1 380.ba odd 18 1
1520.1.m.a 1 380.bb even 18 1
1805.1.h.a 2 19.e even 9 2
1805.1.h.a 2 19.f odd 18 2
1805.1.h.a 2 95.o odd 18 2
1805.1.h.a 2 95.p even 18 2
1805.1.o.a 6 1.a even 1 1 trivial
1805.1.o.a 6 5.b even 2 1 RM
1805.1.o.a 6 19.b odd 2 1 CM
1805.1.o.a 6 19.c even 3 2 inner
1805.1.o.a 6 19.d odd 6 2 inner
1805.1.o.a 6 19.e even 9 3 inner
1805.1.o.a 6 19.f odd 18 3 inner
1805.1.o.a 6 95.d odd 2 1 CM
1805.1.o.a 6 95.h odd 6 2 inner
1805.1.o.a 6 95.i even 6 2 inner
1805.1.o.a 6 95.o odd 18 3 inner
1805.1.o.a 6 95.p even 18 3 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{1}^{\mathrm{new}}(1805, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{6} \) Copy content Toggle raw display
$3$ \( T^{6} \) Copy content Toggle raw display
$5$ \( T^{6} + T^{3} + 1 \) Copy content Toggle raw display
$7$ \( T^{6} \) Copy content Toggle raw display
$11$ \( (T^{2} - 2 T + 4)^{3} \) Copy content Toggle raw display
$13$ \( T^{6} \) Copy content Toggle raw display
$17$ \( T^{6} \) Copy content Toggle raw display
$19$ \( T^{6} \) Copy content Toggle raw display
$23$ \( T^{6} \) Copy content Toggle raw display
$29$ \( T^{6} \) Copy content Toggle raw display
$31$ \( T^{6} \) Copy content Toggle raw display
$37$ \( T^{6} \) Copy content Toggle raw display
$41$ \( T^{6} \) Copy content Toggle raw display
$43$ \( T^{6} \) Copy content Toggle raw display
$47$ \( T^{6} \) Copy content Toggle raw display
$53$ \( T^{6} \) Copy content Toggle raw display
$59$ \( T^{6} \) Copy content Toggle raw display
$61$ \( T^{6} - 8T^{3} + 64 \) Copy content Toggle raw display
$67$ \( T^{6} \) Copy content Toggle raw display
$71$ \( T^{6} \) Copy content Toggle raw display
$73$ \( T^{6} \) Copy content Toggle raw display
$79$ \( T^{6} \) Copy content Toggle raw display
$83$ \( T^{6} \) Copy content Toggle raw display
$89$ \( T^{6} \) Copy content Toggle raw display
$97$ \( T^{6} \) Copy content Toggle raw display
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