Properties

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

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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: \(\Q(\sqrt{73}) \)
Defining polynomial: \( x^{2} - x - 18 \) 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 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{73})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + (\beta + 1) q^{3} + 5 q^{5} + (\beta + 8) q^{7} + (3 \beta - 8) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + (\beta + 1) q^{3} + 5 q^{5} + (\beta + 8) q^{7} + (3 \beta - 8) q^{9} + ( - 10 \beta - 4) q^{11} + (9 \beta - 9) q^{13} + (5 \beta + 5) q^{15} + ( - 11 \beta - 34) q^{17} + ( - 10 \beta - 12) q^{19} + (10 \beta + 26) q^{21} + 23 q^{23} + 25 q^{25} + ( - 29 \beta + 19) q^{27} + ( - 2 \beta - 55) q^{29} + (26 \beta + 33) q^{31} + ( - 24 \beta - 184) q^{33} + (5 \beta + 40) q^{35} + ( - 7 \beta - 242) q^{37} + (9 \beta + 153) q^{39} + ( - 74 \beta - 129) q^{41} + (22 \beta + 166) q^{43} + (15 \beta - 40) q^{45} + (5 \beta + 297) q^{47} + (17 \beta - 261) q^{49} + ( - 56 \beta - 232) q^{51} + (7 \beta - 156) q^{53} + ( - 50 \beta - 20) q^{55} + ( - 32 \beta - 192) q^{57} + ( - 105 \beta - 126) q^{59} + (12 \beta - 92) q^{61} + (19 \beta - 10) q^{63} + (45 \beta - 45) q^{65} + ( - 41 \beta + 286) q^{67} + (23 \beta + 23) q^{69} + (104 \beta - 679) q^{71} + (23 \beta - 183) q^{73} + (25 \beta + 25) q^{75} + ( - 94 \beta - 212) q^{77} + (56 \beta + 16) q^{79} + ( - 120 \beta - 287) q^{81} + ( - 117 \beta - 578) q^{83} + ( - 55 \beta - 170) q^{85} + ( - 59 \beta - 91) q^{87} + ( - 18 \beta + 562) q^{89} + (72 \beta + 90) q^{91} + (85 \beta + 501) q^{93} + ( - 50 \beta - 60) q^{95} + ( - 164 \beta - 1038) q^{97} + (38 \beta - 508) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 10 q^{5} + 17 q^{7} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 10 q^{5} + 17 q^{7} - 13 q^{9} - 18 q^{11} - 9 q^{13} + 15 q^{15} - 79 q^{17} - 34 q^{19} + 62 q^{21} + 46 q^{23} + 50 q^{25} + 9 q^{27} - 112 q^{29} + 92 q^{31} - 392 q^{33} + 85 q^{35} - 491 q^{37} + 315 q^{39} - 332 q^{41} + 354 q^{43} - 65 q^{45} + 599 q^{47} - 505 q^{49} - 520 q^{51} - 305 q^{53} - 90 q^{55} - 416 q^{57} - 357 q^{59} - 172 q^{61} - q^{63} - 45 q^{65} + 531 q^{67} + 69 q^{69} - 1254 q^{71} - 343 q^{73} + 75 q^{75} - 518 q^{77} + 88 q^{79} - 694 q^{81} - 1273 q^{83} - 395 q^{85} - 241 q^{87} + 1106 q^{89} + 252 q^{91} + 1087 q^{93} - 170 q^{95} - 2240 q^{97} - 978 q^{99}+O(q^{100}) \) 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
−3.77200
4.77200
0 −2.77200 0 5.00000 0 4.22800 0 −19.3160 0
1.2 0 5.77200 0 5.00000 0 12.7720 0 6.31601 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.i 2
4.b odd 2 1 230.4.a.f 2
12.b even 2 1 2070.4.a.s 2
20.d odd 2 1 1150.4.a.l 2
20.e even 4 2 1150.4.b.k 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.f 2 4.b odd 2 1
1150.4.a.l 2 20.d odd 2 1
1150.4.b.k 4 20.e even 4 2
1840.4.a.i 2 1.a even 1 1 trivial
2070.4.a.s 2 12.b even 2 1

Hecke kernels

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

\( T_{3}^{2} - 3T_{3} - 16 \) Copy content Toggle raw display
\( T_{7}^{2} - 17T_{7} + 54 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{2} \) Copy content Toggle raw display
$3$ \( T^{2} - 3T - 16 \) Copy content Toggle raw display
$5$ \( (T - 5)^{2} \) Copy content Toggle raw display
$7$ \( T^{2} - 17T + 54 \) Copy content Toggle raw display
$11$ \( T^{2} + 18T - 1744 \) Copy content Toggle raw display
$13$ \( T^{2} + 9T - 1458 \) Copy content Toggle raw display
$17$ \( T^{2} + 79T - 648 \) Copy content Toggle raw display
$19$ \( T^{2} + 34T - 1536 \) Copy content Toggle raw display
$23$ \( (T - 23)^{2} \) Copy content Toggle raw display
$29$ \( T^{2} + 112T + 3063 \) Copy content Toggle raw display
$31$ \( T^{2} - 92T - 10221 \) Copy content Toggle raw display
$37$ \( T^{2} + 491T + 59376 \) Copy content Toggle raw display
$41$ \( T^{2} + 332T - 72381 \) Copy content Toggle raw display
$43$ \( T^{2} - 354T + 22496 \) Copy content Toggle raw display
$47$ \( T^{2} - 599T + 89244 \) Copy content Toggle raw display
$53$ \( T^{2} + 305T + 22362 \) Copy content Toggle raw display
$59$ \( T^{2} + 357T - 169344 \) Copy content Toggle raw display
$61$ \( T^{2} + 172T + 4768 \) Copy content Toggle raw display
$67$ \( T^{2} - 531T + 39812 \) Copy content Toggle raw display
$71$ \( T^{2} + 1254 T + 195737 \) Copy content Toggle raw display
$73$ \( T^{2} + 343T + 19758 \) Copy content Toggle raw display
$79$ \( T^{2} - 88T - 55296 \) Copy content Toggle raw display
$83$ \( T^{2} + 1273 T + 155308 \) Copy content Toggle raw display
$89$ \( T^{2} - 1106 T + 299896 \) Copy content Toggle raw display
$97$ \( T^{2} + 2240 T + 763548 \) Copy content Toggle raw display
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