# Properties

 Label 1900.3.g.c Level $1900$ Weight $3$ Character orbit 1900.g Analytic conductor $51.771$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1900.g (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$51.7712502285$$ Analytic rank: $$0$$ Dimension: $$24$$ Twist minimal: no (minimal twist has level 380) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$24q + 32q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 32q^{9} - 64q^{11} - 48q^{19} - 248q^{39} + 48q^{49} + 304q^{61} - 936q^{81} - 784q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
949.1 0 −4.83157 0 0 0 3.72856i 0 14.3441 0
949.2 0 −4.83157 0 0 0 3.72856i 0 14.3441 0
949.3 0 −3.53755 0 0 0 0.468611i 0 3.51429 0
949.4 0 −3.53755 0 0 0 0.468611i 0 3.51429 0
949.5 0 −3.42504 0 0 0 9.18599i 0 2.73093 0
949.6 0 −3.42504 0 0 0 9.18599i 0 2.73093 0
949.7 0 −3.14288 0 0 0 12.2192i 0 0.877687 0
949.8 0 −3.14288 0 0 0 12.2192i 0 0.877687 0
949.9 0 −2.03369 0 0 0 4.27843i 0 −4.86411 0
949.10 0 −2.03369 0 0 0 4.27843i 0 −4.86411 0
949.11 0 −0.630185 0 0 0 3.98530i 0 −8.60287 0
949.12 0 −0.630185 0 0 0 3.98530i 0 −8.60287 0
949.13 0 0.630185 0 0 0 3.98530i 0 −8.60287 0
949.14 0 0.630185 0 0 0 3.98530i 0 −8.60287 0
949.15 0 2.03369 0 0 0 4.27843i 0 −4.86411 0
949.16 0 2.03369 0 0 0 4.27843i 0 −4.86411 0
949.17 0 3.14288 0 0 0 12.2192i 0 0.877687 0
949.18 0 3.14288 0 0 0 12.2192i 0 0.877687 0
949.19 0 3.42504 0 0 0 9.18599i 0 2.73093 0
949.20 0 3.42504 0 0 0 9.18599i 0 2.73093 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 949.24 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.b odd 2 1 inner
95.d odd 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1900.3.g.c 24
5.b even 2 1 inner 1900.3.g.c 24
5.c odd 4 1 380.3.e.a 12
5.c odd 4 1 1900.3.e.f 12
15.e even 4 1 3420.3.o.a 12
19.b odd 2 1 inner 1900.3.g.c 24
20.e even 4 1 1520.3.h.b 12
95.d odd 2 1 inner 1900.3.g.c 24
95.g even 4 1 380.3.e.a 12
95.g even 4 1 1900.3.e.f 12
285.j odd 4 1 3420.3.o.a 12
380.j odd 4 1 1520.3.h.b 12

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
380.3.e.a 12 5.c odd 4 1
380.3.e.a 12 95.g even 4 1
1520.3.h.b 12 20.e even 4 1
1520.3.h.b 12 380.j odd 4 1
1900.3.e.f 12 5.c odd 4 1
1900.3.e.f 12 95.g even 4 1
1900.3.g.c 24 1.a even 1 1 trivial
1900.3.g.c 24 5.b even 2 1 inner
1900.3.g.c 24 19.b odd 2 1 inner
1900.3.g.c 24 95.d odd 2 1 inner
3420.3.o.a 12 15.e even 4 1
3420.3.o.a 12 285.j odd 4 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{12} - 62 T_{3}^{10} + 1445 T_{3}^{8} - 15924 T_{3}^{6} + 83244 T_{3}^{4} - 170640 T_{3}^{2} + 55600$$ acting on $$S_{3}^{\mathrm{new}}(1900, [\chi])$$.