Properties

 Label 3850.2.a.u Level $3850$ Weight $2$ Character orbit 3850.a Self dual yes Analytic conductor $30.742$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3850.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$30.7424047782$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} + O(q^{10})$$ $$q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} - q^{11} - 2q^{13} + q^{14} + q^{16} + 4q^{17} - 3q^{18} - 6q^{19} - q^{22} - 4q^{23} - 2q^{26} + q^{28} - 2q^{29} - 2q^{31} + q^{32} + 4q^{34} - 3q^{36} - 10q^{37} - 6q^{38} + 4q^{41} + 8q^{43} - q^{44} - 4q^{46} - 2q^{47} + q^{49} - 2q^{52} - 6q^{53} + q^{56} - 2q^{58} - 12q^{59} - 14q^{61} - 2q^{62} - 3q^{63} + q^{64} + 12q^{67} + 4q^{68} - 8q^{71} - 3q^{72} - 4q^{73} - 10q^{74} - 6q^{76} - q^{77} + 9q^{81} + 4q^{82} + 6q^{83} + 8q^{86} - q^{88} - 6q^{89} - 2q^{91} - 4q^{92} - 2q^{94} + 14q^{97} + q^{98} + 3q^{99} + O(q^{100})$$

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 0 1.00000 0 0 1.00000 1.00000 −3.00000 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
$$2$$ $$-1$$
$$5$$ $$1$$
$$7$$ $$-1$$
$$11$$ $$1$$

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 3850.2.a.u 1
5.b even 2 1 154.2.a.a 1
5.c odd 4 2 3850.2.c.j 2
15.d odd 2 1 1386.2.a.l 1
20.d odd 2 1 1232.2.a.e 1
35.c odd 2 1 1078.2.a.d 1
35.i odd 6 2 1078.2.e.i 2
35.j even 6 2 1078.2.e.j 2
40.e odd 2 1 4928.2.a.w 1
40.f even 2 1 4928.2.a.v 1
55.d odd 2 1 1694.2.a.g 1
105.g even 2 1 9702.2.a.ba 1
140.c even 2 1 8624.2.a.r 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.a 1 5.b even 2 1
1078.2.a.d 1 35.c odd 2 1
1078.2.e.i 2 35.i odd 6 2
1078.2.e.j 2 35.j even 6 2
1232.2.a.e 1 20.d odd 2 1
1386.2.a.l 1 15.d odd 2 1
1694.2.a.g 1 55.d odd 2 1
3850.2.a.u 1 1.a even 1 1 trivial
3850.2.c.j 2 5.c odd 4 2
4928.2.a.v 1 40.f even 2 1
4928.2.a.w 1 40.e odd 2 1
8624.2.a.r 1 140.c even 2 1
9702.2.a.ba 1 105.g even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(3850))$$:

 $$T_{3}$$ $$T_{13} + 2$$ $$T_{17} - 4$$ $$T_{19} + 6$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$-1 + T$$
$3$ $$T$$
$5$ $$T$$
$7$ $$-1 + T$$
$11$ $$1 + T$$
$13$ $$2 + T$$
$17$ $$-4 + T$$
$19$ $$6 + T$$
$23$ $$4 + T$$
$29$ $$2 + T$$
$31$ $$2 + T$$
$37$ $$10 + T$$
$41$ $$-4 + T$$
$43$ $$-8 + T$$
$47$ $$2 + T$$
$53$ $$6 + T$$
$59$ $$12 + T$$
$61$ $$14 + T$$
$67$ $$-12 + T$$
$71$ $$8 + T$$
$73$ $$4 + T$$
$79$ $$T$$
$83$ $$-6 + T$$
$89$ $$6 + T$$
$97$ $$-14 + T$$