Properties

 Label 3825.2.a.d Level $3825$ Weight $2$ Character orbit 3825.a Self dual yes Analytic conductor $30.543$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$3825 = 3^{2} \cdot 5^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3825.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$30.5427787731$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 17) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} - q^{4} - 4 q^{7} + 3 q^{8}+O(q^{10})$$ q - q^2 - q^4 - 4 * q^7 + 3 * q^8 $$q - q^{2} - q^{4} - 4 q^{7} + 3 q^{8} + 2 q^{13} + 4 q^{14} - q^{16} + q^{17} - 4 q^{19} + 4 q^{23} - 2 q^{26} + 4 q^{28} - 6 q^{29} + 4 q^{31} - 5 q^{32} - q^{34} + 2 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} - 4 q^{46} + 9 q^{49} - 2 q^{52} + 6 q^{53} - 12 q^{56} + 6 q^{58} + 12 q^{59} - 10 q^{61} - 4 q^{62} + 7 q^{64} - 4 q^{67} - q^{68} + 4 q^{71} + 6 q^{73} - 2 q^{74} + 4 q^{76} + 12 q^{79} - 6 q^{82} - 4 q^{83} + 4 q^{86} - 10 q^{89} - 8 q^{91} - 4 q^{92} - 2 q^{97} - 9 q^{98}+O(q^{100})$$ q - q^2 - q^4 - 4 * q^7 + 3 * q^8 + 2 * q^13 + 4 * q^14 - q^16 + q^17 - 4 * q^19 + 4 * q^23 - 2 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - 5 * q^32 - q^34 + 2 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 - 4 * q^46 + 9 * q^49 - 2 * q^52 + 6 * q^53 - 12 * q^56 + 6 * q^58 + 12 * q^59 - 10 * q^61 - 4 * q^62 + 7 * q^64 - 4 * q^67 - q^68 + 4 * q^71 + 6 * q^73 - 2 * q^74 + 4 * q^76 + 12 * q^79 - 6 * q^82 - 4 * q^83 + 4 * q^86 - 10 * q^89 - 8 * q^91 - 4 * q^92 - 2 * q^97 - 9 * q^98

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 −4.00000 3.00000 0 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
$$3$$ $$-1$$
$$5$$ $$1$$
$$17$$ $$-1$$

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 3825.2.a.d 1
3.b odd 2 1 425.2.a.d 1
5.b even 2 1 153.2.a.c 1
12.b even 2 1 6800.2.a.n 1
15.d odd 2 1 17.2.a.a 1
15.e even 4 2 425.2.b.b 2
20.d odd 2 1 2448.2.a.o 1
35.c odd 2 1 7497.2.a.l 1
40.e odd 2 1 9792.2.a.i 1
40.f even 2 1 9792.2.a.n 1
51.c odd 2 1 7225.2.a.g 1
60.h even 2 1 272.2.a.b 1
85.c even 2 1 2601.2.a.g 1
105.g even 2 1 833.2.a.a 1
105.o odd 6 2 833.2.e.b 2
105.p even 6 2 833.2.e.a 2
120.i odd 2 1 1088.2.a.i 1
120.m even 2 1 1088.2.a.h 1
165.d even 2 1 2057.2.a.e 1
195.e odd 2 1 2873.2.a.c 1
255.h odd 2 1 289.2.a.a 1
255.i odd 4 2 289.2.b.a 2
255.y odd 8 4 289.2.c.a 4
255.be even 16 8 289.2.d.d 8
285.b even 2 1 6137.2.a.b 1
345.h even 2 1 8993.2.a.a 1
1020.b even 2 1 4624.2.a.d 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
17.2.a.a 1 15.d odd 2 1
153.2.a.c 1 5.b even 2 1
272.2.a.b 1 60.h even 2 1
289.2.a.a 1 255.h odd 2 1
289.2.b.a 2 255.i odd 4 2
289.2.c.a 4 255.y odd 8 4
289.2.d.d 8 255.be even 16 8
425.2.a.d 1 3.b odd 2 1
425.2.b.b 2 15.e even 4 2
833.2.a.a 1 105.g even 2 1
833.2.e.a 2 105.p even 6 2
833.2.e.b 2 105.o odd 6 2
1088.2.a.h 1 120.m even 2 1
1088.2.a.i 1 120.i odd 2 1
2057.2.a.e 1 165.d even 2 1
2448.2.a.o 1 20.d odd 2 1
2601.2.a.g 1 85.c even 2 1
2873.2.a.c 1 195.e odd 2 1
3825.2.a.d 1 1.a even 1 1 trivial
4624.2.a.d 1 1020.b even 2 1
6137.2.a.b 1 285.b even 2 1
6800.2.a.n 1 12.b even 2 1
7225.2.a.g 1 51.c odd 2 1
7497.2.a.l 1 35.c odd 2 1
8993.2.a.a 1 345.h even 2 1
9792.2.a.i 1 40.e odd 2 1
9792.2.a.n 1 40.f even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(3825))$$:

 $$T_{2} + 1$$ T2 + 1 $$T_{7} + 4$$ T7 + 4 $$T_{11}$$ T11

Hecke characteristic polynomials

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