# Properties

 Label 1183.2.c.j Level $1183$ Weight $2$ Character orbit 1183.c Analytic conductor $9.446$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1183 = 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1183.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$9.44630255912$$ Analytic rank: $$0$$ Dimension: $$24$$ Twist minimal: yes 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10})$$ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100})$$ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

## 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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
337.1 2.62803i −1.76762 −4.90656 2.94291i 4.64535i 1.00000i 7.63852i 0.124466 7.73406
337.2 2.58557i 2.93994 −4.68518 1.26031i 7.60143i 1.00000i 6.94272i 5.64327 3.25863
337.3 2.47725i 0.982981 −4.13677 1.35413i 2.43509i 1.00000i 5.29330i −2.03375 −3.35452
337.4 2.23724i 3.02592 −3.00523 3.28547i 6.76971i 1.00000i 2.24893i 6.15622 7.35037
337.5 2.07140i −3.01646 −2.29068 2.69245i 6.24828i 1.00000i 0.602118i 6.09903 −5.57713
337.6 2.06743i 2.11889 −2.27425 2.43928i 4.38065i 1.00000i 0.566992i 1.48970 −5.04303
337.7 1.35819i 3.39737 0.155322 0.772491i 4.61428i 1.00000i 2.92733i 8.54215 −1.04919
337.8 1.10989i 0.955760 0.768150 3.55862i 1.06079i 1.00000i 3.07233i −2.08652 −3.94966
337.9 0.983820i −1.57171 1.03210 0.398447i 1.54628i 1.00000i 2.98304i −0.529731 −0.392000
337.10 0.961590i −1.98737 1.07534 3.39320i 1.91103i 1.00000i 2.95722i 0.949635 3.26287
337.11 0.842530i 0.161973 1.29014 3.72786i 0.136467i 1.00000i 2.77204i −2.97376 3.14083
337.12 0.149660i 2.76031 1.97760 4.13443i 0.413107i 1.00000i 0.595288i 4.61930 0.618759
337.13 0.149660i 2.76031 1.97760 4.13443i 0.413107i 1.00000i 0.595288i 4.61930 0.618759
337.14 0.842530i 0.161973 1.29014 3.72786i 0.136467i 1.00000i 2.77204i −2.97376 3.14083
337.15 0.961590i −1.98737 1.07534 3.39320i 1.91103i 1.00000i 2.95722i 0.949635 3.26287
337.16 0.983820i −1.57171 1.03210 0.398447i 1.54628i 1.00000i 2.98304i −0.529731 −0.392000
337.17 1.10989i 0.955760 0.768150 3.55862i 1.06079i 1.00000i 3.07233i −2.08652 −3.94966
337.18 1.35819i 3.39737 0.155322 0.772491i 4.61428i 1.00000i 2.92733i 8.54215 −1.04919
337.19 2.06743i 2.11889 −2.27425 2.43928i 4.38065i 1.00000i 0.566992i 1.48970 −5.04303
337.20 2.07140i −3.01646 −2.29068 2.69245i 6.24828i 1.00000i 0.602118i 6.09903 −5.57713
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 337.24 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.b even 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1183.2.c.j 24
13.b even 2 1 inner 1183.2.c.j 24
13.d odd 4 1 1183.2.a.q 12
13.d odd 4 1 1183.2.a.r yes 12
91.i even 4 1 8281.2.a.cn 12
91.i even 4 1 8281.2.a.cq 12

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1183.2.a.q 12 13.d odd 4 1
1183.2.a.r yes 12 13.d odd 4 1
1183.2.c.j 24 1.a even 1 1 trivial
1183.2.c.j 24 13.b even 2 1 inner
8281.2.a.cn 12 91.i even 4 1
8281.2.a.cq 12 91.i even 4 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{24} + 39 T_{2}^{22} + 661 T_{2}^{20} + 6390 T_{2}^{18} + 38898 T_{2}^{16} + 155486 T_{2}^{14} + 413755 T_{2}^{12} + 729610 T_{2}^{10} + 835014 T_{2}^{8} + 593266 T_{2}^{6} + 238217 T_{2}^{4} + 42595 T_{2}^{2} + \cdots + 841$$ acting on $$S_{2}^{\mathrm{new}}(1183, [\chi])$$.