# Properties

 Label 1925.2.a.c Level 1925 Weight 2 Character orbit 1925.a Self dual yes Analytic conductor 15.371 Analytic rank 1 Dimension 1 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1925 = 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1925.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$15.3712023891$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 77) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + O(q^{10})$$ $$q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + q^{11} + 2q^{12} - 4q^{13} - q^{14} - q^{16} - 4q^{17} - q^{18} - 2q^{21} - q^{22} + 4q^{23} - 6q^{24} + 4q^{26} + 4q^{27} - q^{28} - 6q^{29} + 10q^{31} - 5q^{32} - 2q^{33} + 4q^{34} - q^{36} + 6q^{37} + 8q^{39} + 4q^{41} + 2q^{42} - 12q^{43} - q^{44} - 4q^{46} + 10q^{47} + 2q^{48} + q^{49} + 8q^{51} + 4q^{52} + 6q^{53} - 4q^{54} + 3q^{56} + 6q^{58} + 2q^{59} - 10q^{62} + q^{63} + 7q^{64} + 2q^{66} - 8q^{67} + 4q^{68} - 8q^{69} - 12q^{71} + 3q^{72} + 8q^{73} - 6q^{74} + q^{77} - 8q^{78} + 8q^{79} - 11q^{81} - 4q^{82} + 2q^{84} + 12q^{86} + 12q^{87} + 3q^{88} - 6q^{89} - 4q^{91} - 4q^{92} - 20q^{93} - 10q^{94} + 10q^{96} + 10q^{97} - q^{98} + q^{99} + O(q^{100})$$

## 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 −2.00000 −1.00000 0 2.00000 1.00000 3.00000 1.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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 1925.2.a.c 1
5.b even 2 1 77.2.a.c 1
5.c odd 4 2 1925.2.b.d 2
15.d odd 2 1 693.2.a.a 1
20.d odd 2 1 1232.2.a.a 1
35.c odd 2 1 539.2.a.d 1
35.i odd 6 2 539.2.e.b 2
35.j even 6 2 539.2.e.a 2
40.e odd 2 1 4928.2.a.bi 1
40.f even 2 1 4928.2.a.g 1
55.d odd 2 1 847.2.a.a 1
55.h odd 10 4 847.2.f.k 4
55.j even 10 4 847.2.f.e 4
105.g even 2 1 4851.2.a.a 1
140.c even 2 1 8624.2.a.bc 1
165.d even 2 1 7623.2.a.n 1
385.h even 2 1 5929.2.a.b 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
77.2.a.c 1 5.b even 2 1
539.2.a.d 1 35.c odd 2 1
539.2.e.a 2 35.j even 6 2
539.2.e.b 2 35.i odd 6 2
693.2.a.a 1 15.d odd 2 1
847.2.a.a 1 55.d odd 2 1
847.2.f.e 4 55.j even 10 4
847.2.f.k 4 55.h odd 10 4
1232.2.a.a 1 20.d odd 2 1
1925.2.a.c 1 1.a even 1 1 trivial
1925.2.b.d 2 5.c odd 4 2
4851.2.a.a 1 105.g even 2 1
4928.2.a.g 1 40.f even 2 1
4928.2.a.bi 1 40.e odd 2 1
5929.2.a.b 1 385.h even 2 1
7623.2.a.n 1 165.d even 2 1
8624.2.a.bc 1 140.c even 2 1

## Atkin-Lehner signs

$$p$$ Sign
$$5$$ $$1$$
$$7$$ $$-1$$
$$11$$ $$-1$$

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(1925))$$:

 $$T_{2} + 1$$ $$T_{3} + 2$$ $$T_{13} + 4$$

## Hecke characteristic polynomials

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