# Properties

 Label 1850.2.a.c Level $1850$ Weight $2$ Character orbit 1850.a Self dual yes Analytic conductor $14.772$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1850 = 2 \cdot 5^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1850.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$14.7723243739$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} - q^{3} + q^{4} + q^{6} + 4 q^{7} - q^{8} - 2 q^{9}+O(q^{10})$$ q - q^2 - q^3 + q^4 + q^6 + 4 * q^7 - q^8 - 2 * q^9 $$q - q^{2} - q^{3} + q^{4} + q^{6} + 4 q^{7} - q^{8} - 2 q^{9} + 3 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{16} + 3 q^{17} + 2 q^{18} - 3 q^{19} - 4 q^{21} - 3 q^{22} + 2 q^{23} + q^{24} - 6 q^{26} + 5 q^{27} + 4 q^{28} - q^{32} - 3 q^{33} - 3 q^{34} - 2 q^{36} - q^{37} + 3 q^{38} - 6 q^{39} - 3 q^{41} + 4 q^{42} - 4 q^{43} + 3 q^{44} - 2 q^{46} + 4 q^{47} - q^{48} + 9 q^{49} - 3 q^{51} + 6 q^{52} - 2 q^{53} - 5 q^{54} - 4 q^{56} + 3 q^{57} - 12 q^{59} + 12 q^{61} - 8 q^{63} + q^{64} + 3 q^{66} + 9 q^{67} + 3 q^{68} - 2 q^{69} - 2 q^{71} + 2 q^{72} - 9 q^{73} + q^{74} - 3 q^{76} + 12 q^{77} + 6 q^{78} - 2 q^{79} + q^{81} + 3 q^{82} - 7 q^{83} - 4 q^{84} + 4 q^{86} - 3 q^{88} - 3 q^{89} + 24 q^{91} + 2 q^{92} - 4 q^{94} + q^{96} + 2 q^{97} - 9 q^{98} - 6 q^{99}+O(q^{100})$$ q - q^2 - q^3 + q^4 + q^6 + 4 * q^7 - q^8 - 2 * q^9 + 3 * q^11 - q^12 + 6 * q^13 - 4 * q^14 + q^16 + 3 * q^17 + 2 * q^18 - 3 * q^19 - 4 * q^21 - 3 * q^22 + 2 * q^23 + q^24 - 6 * q^26 + 5 * q^27 + 4 * q^28 - q^32 - 3 * q^33 - 3 * q^34 - 2 * q^36 - q^37 + 3 * q^38 - 6 * q^39 - 3 * q^41 + 4 * q^42 - 4 * q^43 + 3 * q^44 - 2 * q^46 + 4 * q^47 - q^48 + 9 * q^49 - 3 * q^51 + 6 * q^52 - 2 * q^53 - 5 * q^54 - 4 * q^56 + 3 * q^57 - 12 * q^59 + 12 * q^61 - 8 * q^63 + q^64 + 3 * q^66 + 9 * q^67 + 3 * q^68 - 2 * q^69 - 2 * q^71 + 2 * q^72 - 9 * q^73 + q^74 - 3 * q^76 + 12 * q^77 + 6 * q^78 - 2 * q^79 + q^81 + 3 * q^82 - 7 * q^83 - 4 * q^84 + 4 * q^86 - 3 * q^88 - 3 * q^89 + 24 * q^91 + 2 * q^92 - 4 * q^94 + q^96 + 2 * q^97 - 9 * q^98 - 6 * 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
−1.00000 −1.00000 1.00000 0 1.00000 4.00000 −1.00000 −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
$$2$$ $$1$$
$$5$$ $$-1$$
$$37$$ $$1$$

## 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 1850.2.a.c 1
5.b even 2 1 1850.2.a.m yes 1
5.c odd 4 2 1850.2.b.e 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1850.2.a.c 1 1.a even 1 1 trivial
1850.2.a.m yes 1 5.b even 2 1
1850.2.b.e 2 5.c odd 4 2

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(1850))$$:

 $$T_{3} + 1$$ T3 + 1 $$T_{7} - 4$$ T7 - 4

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T + 1$$
$3$ $$T + 1$$
$5$ $$T$$
$7$ $$T - 4$$
$11$ $$T - 3$$
$13$ $$T - 6$$
$17$ $$T - 3$$
$19$ $$T + 3$$
$23$ $$T - 2$$
$29$ $$T$$
$31$ $$T$$
$37$ $$T + 1$$
$41$ $$T + 3$$
$43$ $$T + 4$$
$47$ $$T - 4$$
$53$ $$T + 2$$
$59$ $$T + 12$$
$61$ $$T - 12$$
$67$ $$T - 9$$
$71$ $$T + 2$$
$73$ $$T + 9$$
$79$ $$T + 2$$
$83$ $$T + 7$$
$89$ $$T + 3$$
$97$ $$T - 2$$