Properties

Label 1840.4.a.h
Level $1840$
Weight $4$
Character orbit 1840.a
Self dual yes
Analytic conductor $108.564$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(108.563514411\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{109}) \)
Defining polynomial: \( x^{2} - x - 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{109})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + (\beta + 1) q^{3} + 5 q^{5} + ( - 5 \beta + 2) q^{7} + (3 \beta + 1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + (\beta + 1) q^{3} + 5 q^{5} + ( - 5 \beta + 2) q^{7} + (3 \beta + 1) q^{9} + (5 \beta + 11) q^{11} + ( - 3 \beta - 6) q^{13} + (5 \beta + 5) q^{15} + (7 \beta - 43) q^{17} + ( - 13 \beta + 42) q^{19} + ( - 8 \beta - 133) q^{21} + 23 q^{23} + 25 q^{25} + ( - 20 \beta + 55) q^{27} + (10 \beta - 220) q^{29} + (17 \beta + 144) q^{31} + (21 \beta + 146) q^{33} + ( - 25 \beta + 10) q^{35} + ( - 28 \beta - 20) q^{37} + ( - 12 \beta - 87) q^{39} + ( - 11 \beta - 291) q^{41} + ( - 8 \beta - 320) q^{43} + (15 \beta + 5) q^{45} + (74 \beta - 228) q^{47} + (5 \beta + 336) q^{49} + ( - 29 \beta + 146) q^{51} + ( - 44 \beta - 210) q^{53} + (25 \beta + 55) q^{55} + (16 \beta - 309) q^{57} + (54 \beta - 18) q^{59} + ( - 57 \beta + 25) q^{61} + ( - 14 \beta - 403) q^{63} + ( - 15 \beta - 30) q^{65} + (76 \beta - 68) q^{67} + (23 \beta + 23) q^{69} + ( - 97 \beta + 563) q^{71} + (62 \beta + 6) q^{73} + (25 \beta + 25) q^{75} + ( - 70 \beta - 653) q^{77} + ( - 172 \beta - 260) q^{79} + ( - 66 \beta - 512) q^{81} + (144 \beta + 658) q^{83} + (35 \beta - 215) q^{85} + ( - 200 \beta + 50) q^{87} + (180 \beta - 200) q^{89} + (39 \beta + 393) q^{91} + (178 \beta + 603) q^{93} + ( - 65 \beta + 210) q^{95} + ( - 203 \beta + 771) q^{97} + (53 \beta + 416) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 10 q^{5} - q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 10 q^{5} - q^{7} + 5 q^{9} + 27 q^{11} - 15 q^{13} + 15 q^{15} - 79 q^{17} + 71 q^{19} - 274 q^{21} + 46 q^{23} + 50 q^{25} + 90 q^{27} - 430 q^{29} + 305 q^{31} + 313 q^{33} - 5 q^{35} - 68 q^{37} - 186 q^{39} - 593 q^{41} - 648 q^{43} + 25 q^{45} - 382 q^{47} + 677 q^{49} + 263 q^{51} - 464 q^{53} + 135 q^{55} - 602 q^{57} + 18 q^{59} - 7 q^{61} - 820 q^{63} - 75 q^{65} - 60 q^{67} + 69 q^{69} + 1029 q^{71} + 74 q^{73} + 75 q^{75} - 1376 q^{77} - 692 q^{79} - 1090 q^{81} + 1460 q^{83} - 395 q^{85} - 100 q^{87} - 220 q^{89} + 825 q^{91} + 1384 q^{93} + 355 q^{95} + 1339 q^{97} + 885 q^{99}+O(q^{100}) \) 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
−4.72015
5.72015
0 −3.72015 0 5.00000 0 25.6008 0 −13.1605 0
1.2 0 6.72015 0 5.00000 0 −26.6008 0 18.1605 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(23\) \(-1\)

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 1840.4.a.h 2
4.b odd 2 1 115.4.a.c 2
12.b even 2 1 1035.4.a.g 2
20.d odd 2 1 575.4.a.h 2
20.e even 4 2 575.4.b.f 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.4.a.c 2 4.b odd 2 1
575.4.a.h 2 20.d odd 2 1
575.4.b.f 4 20.e even 4 2
1035.4.a.g 2 12.b even 2 1
1840.4.a.h 2 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\):

\( T_{3}^{2} - 3T_{3} - 25 \) Copy content Toggle raw display
\( T_{7}^{2} + T_{7} - 681 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{2} \) Copy content Toggle raw display
$3$ \( T^{2} - 3T - 25 \) Copy content Toggle raw display
$5$ \( (T - 5)^{2} \) Copy content Toggle raw display
$7$ \( T^{2} + T - 681 \) Copy content Toggle raw display
$11$ \( T^{2} - 27T - 499 \) Copy content Toggle raw display
$13$ \( T^{2} + 15T - 189 \) Copy content Toggle raw display
$17$ \( T^{2} + 79T + 225 \) Copy content Toggle raw display
$19$ \( T^{2} - 71T - 3345 \) Copy content Toggle raw display
$23$ \( (T - 23)^{2} \) Copy content Toggle raw display
$29$ \( T^{2} + 430T + 43500 \) Copy content Toggle raw display
$31$ \( T^{2} - 305T + 15381 \) Copy content Toggle raw display
$37$ \( T^{2} + 68T - 20208 \) Copy content Toggle raw display
$41$ \( T^{2} + 593T + 84615 \) Copy content Toggle raw display
$43$ \( T^{2} + 648T + 103232 \) Copy content Toggle raw display
$47$ \( T^{2} + 382T - 112740 \) Copy content Toggle raw display
$53$ \( T^{2} + 464T + 1068 \) Copy content Toggle raw display
$59$ \( T^{2} - 18T - 79380 \) Copy content Toggle raw display
$61$ \( T^{2} + 7T - 88523 \) Copy content Toggle raw display
$67$ \( T^{2} + 60T - 156496 \) Copy content Toggle raw display
$71$ \( T^{2} - 1029T + 8315 \) Copy content Toggle raw display
$73$ \( T^{2} - 74T - 103380 \) Copy content Toggle raw display
$79$ \( T^{2} + 692T - 686448 \) Copy content Toggle raw display
$83$ \( T^{2} - 1460T - 32156 \) Copy content Toggle raw display
$89$ \( T^{2} + 220T - 870800 \) Copy content Toggle raw display
$97$ \( T^{2} - 1339 T - 674715 \) Copy content Toggle raw display
show more
show less