Properties

Label 1155.2.l.f
Level 1155
Weight 2
Character orbit 1155.l
Analytic conductor 9.223
Analytic rank 0
Dimension 40
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1155.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(40\)
Coefficient ring index: multiple of None
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.

\(\operatorname{Tr}(f)(q) = \) \( 40q + 4q^{2} - 4q^{3} + 44q^{4} + 4q^{6} + 12q^{8} - 2q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q + 4q^{2} - 4q^{3} + 44q^{4} + 4q^{6} + 12q^{8} - 2q^{9} + 6q^{11} + 8q^{12} + 2q^{15} + 68q^{16} - 40q^{18} + 2q^{21} - 4q^{22} + 12q^{24} - 40q^{25} + 32q^{27} + 24q^{29} - 8q^{31} - 52q^{32} + 28q^{33} + 32q^{34} - 40q^{35} - 48q^{37} - 66q^{39} + 16q^{41} - 32q^{44} + 32q^{48} - 40q^{49} - 4q^{50} + 14q^{51} + 72q^{54} + 8q^{55} + 24q^{57} - 80q^{58} + 24q^{60} - 48q^{62} + 76q^{64} - 4q^{65} - 48q^{67} + 32q^{68} - 20q^{69} - 4q^{70} - 128q^{72} + 4q^{75} + 8q^{77} - 28q^{78} + 50q^{81} - 32q^{82} + 24q^{83} + 24q^{84} + 32q^{87} - 16q^{88} - 8q^{90} - 4q^{91} - 20q^{93} + 12q^{95} - 12q^{96} + 100q^{97} - 4q^{98} + 56q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1121.1 −2.72154 −1.44946 0.948193i 5.40675 1.00000i 3.94475 + 2.58054i 1.00000i −9.27160 1.20186 + 2.74873i 2.72154i
1121.2 −2.72154 −1.44946 + 0.948193i 5.40675 1.00000i 3.94475 2.58054i 1.00000i −9.27160 1.20186 2.74873i 2.72154i
1121.3 −2.50847 1.71957 0.207558i 4.29243 1.00000i −4.31349 + 0.520654i 1.00000i −5.75050 2.91384 0.713822i 2.50847i
1121.4 −2.50847 1.71957 + 0.207558i 4.29243 1.00000i −4.31349 0.520654i 1.00000i −5.75050 2.91384 + 0.713822i 2.50847i
1121.5 −2.45082 0.877309 + 1.49343i 4.00650 1.00000i −2.15012 3.66012i 1.00000i −4.91756 −1.46066 + 2.62040i 2.45082i
1121.6 −2.45082 0.877309 1.49343i 4.00650 1.00000i −2.15012 + 3.66012i 1.00000i −4.91756 −1.46066 2.62040i 2.45082i
1121.7 −1.78181 −1.68629 0.395519i 1.17485 1.00000i 3.00464 + 0.704739i 1.00000i 1.47026 2.68713 + 1.33392i 1.78181i
1121.8 −1.78181 −1.68629 + 0.395519i 1.17485 1.00000i 3.00464 0.704739i 1.00000i 1.47026 2.68713 1.33392i 1.78181i
1121.9 −1.41625 −1.72991 + 0.0861016i 0.00575714 1.00000i 2.44998 0.121941i 1.00000i 2.82434 2.98517 0.297896i 1.41625i
1121.10 −1.41625 −1.72991 0.0861016i 0.00575714 1.00000i 2.44998 + 0.121941i 1.00000i 2.82434 2.98517 + 0.297896i 1.41625i
1121.11 −1.30517 −0.259419 1.71251i −0.296539 1.00000i 0.338586 + 2.23512i 1.00000i 2.99737 −2.86540 + 0.888518i 1.30517i
1121.12 −1.30517 −0.259419 + 1.71251i −0.296539 1.00000i 0.338586 2.23512i 1.00000i 2.99737 −2.86540 0.888518i 1.30517i
1121.13 −0.892777 0.497839 1.65896i −1.20295 1.00000i −0.444460 + 1.48108i 1.00000i 2.85952 −2.50431 1.65179i 0.892777i
1121.14 −0.892777 0.497839 + 1.65896i −1.20295 1.00000i −0.444460 1.48108i 1.00000i 2.85952 −2.50431 + 1.65179i 0.892777i
1121.15 −0.490604 1.73069 + 0.0687106i −1.75931 1.00000i −0.849081 0.0337096i 1.00000i 1.84433 2.99056 + 0.237833i 0.490604i
1121.16 −0.490604 1.73069 0.0687106i −1.75931 1.00000i −0.849081 + 0.0337096i 1.00000i 1.84433 2.99056 0.237833i 0.490604i
1121.17 −0.371904 −0.305927 1.70482i −1.86169 1.00000i 0.113775 + 0.634029i 1.00000i 1.43618 −2.81282 + 1.04310i 0.371904i
1121.18 −0.371904 −0.305927 + 1.70482i −1.86169 1.00000i 0.113775 0.634029i 1.00000i 1.43618 −2.81282 1.04310i 0.371904i
1121.19 −0.261999 −0.733531 1.56905i −1.93136 1.00000i 0.192184 + 0.411090i 1.00000i 1.03001 −1.92386 + 2.30190i 0.261999i
1121.20 −0.261999 −0.733531 + 1.56905i −1.93136 1.00000i 0.192184 0.411090i 1.00000i 1.03001 −1.92386 2.30190i 0.261999i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1121.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
33.d even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1155.2.l.f yes 40
3.b odd 2 1 1155.2.l.e 40
11.b odd 2 1 1155.2.l.e 40
33.d even 2 1 inner 1155.2.l.f yes 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.2.l.e 40 3.b odd 2 1
1155.2.l.e 40 11.b odd 2 1
1155.2.l.f yes 40 1.a even 1 1 trivial
1155.2.l.f yes 40 33.d even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1155, [\chi])\):

\(T_{2}^{20} - \cdots\)
\(T_{17}^{20} - \cdots\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database