Properties

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

Related objects

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: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 230) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + 5 q^{3} - 5 q^{5} - 12 q^{7} - 2 q^{9}+O(q^{10})$$ q + 5 * q^3 - 5 * q^5 - 12 * q^7 - 2 * q^9 $$q + 5 q^{3} - 5 q^{5} - 12 q^{7} - 2 q^{9} - 22 q^{11} + 19 q^{13} - 25 q^{15} + 96 q^{17} + 98 q^{19} - 60 q^{21} - 23 q^{23} + 25 q^{25} - 145 q^{27} - 227 q^{29} + 285 q^{31} - 110 q^{33} + 60 q^{35} - 398 q^{37} + 95 q^{39} + 271 q^{41} + 100 q^{43} + 10 q^{45} + 285 q^{47} - 199 q^{49} + 480 q^{51} + 18 q^{53} + 110 q^{55} + 490 q^{57} + 352 q^{59} - 478 q^{61} + 24 q^{63} - 95 q^{65} - 330 q^{67} - 115 q^{69} - 835 q^{71} - 1127 q^{73} + 125 q^{75} + 264 q^{77} - 322 q^{79} - 671 q^{81} - 572 q^{83} - 480 q^{85} - 1135 q^{87} - 504 q^{89} - 228 q^{91} + 1425 q^{93} - 490 q^{95} + 1712 q^{97} + 44 q^{99}+O(q^{100})$$ q + 5 * q^3 - 5 * q^5 - 12 * q^7 - 2 * q^9 - 22 * q^11 + 19 * q^13 - 25 * q^15 + 96 * q^17 + 98 * q^19 - 60 * q^21 - 23 * q^23 + 25 * q^25 - 145 * q^27 - 227 * q^29 + 285 * q^31 - 110 * q^33 + 60 * q^35 - 398 * q^37 + 95 * q^39 + 271 * q^41 + 100 * q^43 + 10 * q^45 + 285 * q^47 - 199 * q^49 + 480 * q^51 + 18 * q^53 + 110 * q^55 + 490 * q^57 + 352 * q^59 - 478 * q^61 + 24 * q^63 - 95 * q^65 - 330 * q^67 - 115 * q^69 - 835 * q^71 - 1127 * q^73 + 125 * q^75 + 264 * q^77 - 322 * q^79 - 671 * q^81 - 572 * q^83 - 480 * q^85 - 1135 * q^87 - 504 * q^89 - 228 * q^91 + 1425 * q^93 - 490 * q^95 + 1712 * q^97 + 44 * q^99

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
0 5.00000 0 −5.00000 0 −12.0000 0 −2.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

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.g 1
4.b odd 2 1 230.4.a.a 1
12.b even 2 1 2070.4.a.o 1
20.d odd 2 1 1150.4.a.i 1
20.e even 4 2 1150.4.b.h 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.a 1 4.b odd 2 1
1150.4.a.i 1 20.d odd 2 1
1150.4.b.h 2 20.e even 4 2
1840.4.a.g 1 1.a even 1 1 trivial
2070.4.a.o 1 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 $$S_{4}^{\mathrm{new}}(\Gamma_0(1840))$$:

 $$T_{3} - 5$$ T3 - 5 $$T_{7} + 12$$ T7 + 12

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T - 5$$
$5$ $$T + 5$$
$7$ $$T + 12$$
$11$ $$T + 22$$
$13$ $$T - 19$$
$17$ $$T - 96$$
$19$ $$T - 98$$
$23$ $$T + 23$$
$29$ $$T + 227$$
$31$ $$T - 285$$
$37$ $$T + 398$$
$41$ $$T - 271$$
$43$ $$T - 100$$
$47$ $$T - 285$$
$53$ $$T - 18$$
$59$ $$T - 352$$
$61$ $$T + 478$$
$67$ $$T + 330$$
$71$ $$T + 835$$
$73$ $$T + 1127$$
$79$ $$T + 322$$
$83$ $$T + 572$$
$89$ $$T + 504$$
$97$ $$T - 1712$$