Properties

Label 1805.4.a.h
Level $1805$
Weight $4$
Character orbit 1805.a
Self dual yes
Analytic conductor $106.498$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(106.498447560\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 4 q^{2} - 2 q^{3} + 8 q^{4} - 5 q^{5} - 8 q^{6} + 6 q^{7} - 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 4 q^{2} - 2 q^{3} + 8 q^{4} - 5 q^{5} - 8 q^{6} + 6 q^{7} - 23 q^{9} - 20 q^{10} + 32 q^{11} - 16 q^{12} + 38 q^{13} + 24 q^{14} + 10 q^{15} - 64 q^{16} + 26 q^{17} - 92 q^{18} - 40 q^{20} - 12 q^{21} + 128 q^{22} - 78 q^{23} + 25 q^{25} + 152 q^{26} + 100 q^{27} + 48 q^{28} + 50 q^{29} + 40 q^{30} + 108 q^{31} - 256 q^{32} - 64 q^{33} + 104 q^{34} - 30 q^{35} - 184 q^{36} - 266 q^{37} - 76 q^{39} - 22 q^{41} - 48 q^{42} + 442 q^{43} + 256 q^{44} + 115 q^{45} - 312 q^{46} - 514 q^{47} + 128 q^{48} - 307 q^{49} + 100 q^{50} - 52 q^{51} + 304 q^{52} - 2 q^{53} + 400 q^{54} - 160 q^{55} + 200 q^{58} - 500 q^{59} + 80 q^{60} - 518 q^{61} + 432 q^{62} - 138 q^{63} - 512 q^{64} - 190 q^{65} - 256 q^{66} - 126 q^{67} + 208 q^{68} + 156 q^{69} - 120 q^{70} - 412 q^{71} - 878 q^{73} - 1064 q^{74} - 50 q^{75} + 192 q^{77} - 304 q^{78} - 600 q^{79} + 320 q^{80} + 421 q^{81} - 88 q^{82} + 282 q^{83} - 96 q^{84} - 130 q^{85} + 1768 q^{86} - 100 q^{87} + 150 q^{89} + 460 q^{90} + 228 q^{91} - 624 q^{92} - 216 q^{93} - 2056 q^{94} + 512 q^{96} - 386 q^{97} - 1228 q^{98} - 736 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
4.00000 −2.00000 8.00000 −5.00000 −8.00000 6.00000 0 −23.0000 −20.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(19\) \(-1\)

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 1805.4.a.h 1
19.b odd 2 1 5.4.a.a 1
57.d even 2 1 45.4.a.d 1
76.d even 2 1 80.4.a.d 1
95.d odd 2 1 25.4.a.c 1
95.g even 4 2 25.4.b.a 2
133.c even 2 1 245.4.a.a 1
133.o even 6 2 245.4.e.g 2
133.r odd 6 2 245.4.e.f 2
152.b even 2 1 320.4.a.h 1
152.g odd 2 1 320.4.a.g 1
171.l even 6 2 405.4.e.c 2
171.o odd 6 2 405.4.e.l 2
209.d even 2 1 605.4.a.d 1
228.b odd 2 1 720.4.a.u 1
247.d odd 2 1 845.4.a.b 1
285.b even 2 1 225.4.a.b 1
285.j odd 4 2 225.4.b.c 2
304.j odd 4 2 1280.4.d.e 2
304.m even 4 2 1280.4.d.l 2
323.c odd 2 1 1445.4.a.a 1
380.d even 2 1 400.4.a.m 1
380.j odd 4 2 400.4.c.k 2
399.h odd 2 1 2205.4.a.q 1
665.g even 2 1 1225.4.a.k 1
760.b odd 2 1 1600.4.a.bi 1
760.p even 2 1 1600.4.a.s 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5.4.a.a 1 19.b odd 2 1
25.4.a.c 1 95.d odd 2 1
25.4.b.a 2 95.g even 4 2
45.4.a.d 1 57.d even 2 1
80.4.a.d 1 76.d even 2 1
225.4.a.b 1 285.b even 2 1
225.4.b.c 2 285.j odd 4 2
245.4.a.a 1 133.c even 2 1
245.4.e.f 2 133.r odd 6 2
245.4.e.g 2 133.o even 6 2
320.4.a.g 1 152.g odd 2 1
320.4.a.h 1 152.b even 2 1
400.4.a.m 1 380.d even 2 1
400.4.c.k 2 380.j odd 4 2
405.4.e.c 2 171.l even 6 2
405.4.e.l 2 171.o odd 6 2
605.4.a.d 1 209.d even 2 1
720.4.a.u 1 228.b odd 2 1
845.4.a.b 1 247.d odd 2 1
1225.4.a.k 1 665.g even 2 1
1280.4.d.e 2 304.j odd 4 2
1280.4.d.l 2 304.m even 4 2
1445.4.a.a 1 323.c odd 2 1
1600.4.a.s 1 760.p even 2 1
1600.4.a.bi 1 760.b odd 2 1
1805.4.a.h 1 1.a even 1 1 trivial
2205.4.a.q 1 399.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1805))\):

\( T_{2} - 4 \) Copy content Toggle raw display
\( T_{3} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 4 \) Copy content Toggle raw display
$3$ \( T + 2 \) Copy content Toggle raw display
$5$ \( T + 5 \) Copy content Toggle raw display
$7$ \( T - 6 \) Copy content Toggle raw display
$11$ \( T - 32 \) Copy content Toggle raw display
$13$ \( T - 38 \) Copy content Toggle raw display
$17$ \( T - 26 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 78 \) Copy content Toggle raw display
$29$ \( T - 50 \) Copy content Toggle raw display
$31$ \( T - 108 \) Copy content Toggle raw display
$37$ \( T + 266 \) Copy content Toggle raw display
$41$ \( T + 22 \) Copy content Toggle raw display
$43$ \( T - 442 \) Copy content Toggle raw display
$47$ \( T + 514 \) Copy content Toggle raw display
$53$ \( T + 2 \) Copy content Toggle raw display
$59$ \( T + 500 \) Copy content Toggle raw display
$61$ \( T + 518 \) Copy content Toggle raw display
$67$ \( T + 126 \) Copy content Toggle raw display
$71$ \( T + 412 \) Copy content Toggle raw display
$73$ \( T + 878 \) Copy content Toggle raw display
$79$ \( T + 600 \) Copy content Toggle raw display
$83$ \( T - 282 \) Copy content Toggle raw display
$89$ \( T - 150 \) Copy content Toggle raw display
$97$ \( T + 386 \) Copy content Toggle raw display
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