Properties

Label 1155.2.l.e
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.

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

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 −2.79309 0.351991 1.69591i 5.80135 1.00000i −0.983141 + 4.73682i 1.00000i −10.6175 −2.75221 1.19389i 2.79309i
1121.2 −2.79309 0.351991 + 1.69591i 5.80135 1.00000i −0.983141 4.73682i 1.00000i −10.6175 −2.75221 + 1.19389i 2.79309i
1121.3 −2.55898 −0.371837 1.69167i 4.54836 1.00000i 0.951521 + 4.32893i 1.00000i −6.52118 −2.72347 + 1.25805i 2.55898i
1121.4 −2.55898 −0.371837 + 1.69167i 4.54836 1.00000i 0.951521 4.32893i 1.00000i −6.52118 −2.72347 1.25805i 2.55898i
1121.5 −2.21445 1.64596 0.539264i 2.90381 1.00000i −3.64491 + 1.19418i 1.00000i −2.00144 2.41839 1.77522i 2.21445i
1121.6 −2.21445 1.64596 + 0.539264i 2.90381 1.00000i −3.64491 1.19418i 1.00000i −2.00144 2.41839 + 1.77522i 2.21445i
1121.7 −2.04560 −1.22443 1.22506i 2.18447 1.00000i 2.50470 + 2.50597i 1.00000i −0.377355 −0.00153018 + 3.00000i 2.04560i
1121.8 −2.04560 −1.22443 + 1.22506i 2.18447 1.00000i 2.50470 2.50597i 1.00000i −0.377355 −0.00153018 3.00000i 2.04560i
1121.9 −1.88704 1.57144 0.728399i 1.56093 1.00000i −2.96538 + 1.37452i 1.00000i 0.828540 1.93887 2.28928i 1.88704i
1121.10 −1.88704 1.57144 + 0.728399i 1.56093 1.00000i −2.96538 1.37452i 1.00000i 0.828540 1.93887 + 2.28928i 1.88704i
1121.11 −1.80850 −1.28663 + 1.15956i 1.27068 1.00000i 2.32688 2.09707i 1.00000i 1.31898 0.310844 2.98385i 1.80850i
1121.12 −1.80850 −1.28663 1.15956i 1.27068 1.00000i 2.32688 + 2.09707i 1.00000i 1.31898 0.310844 + 2.98385i 1.80850i
1121.13 −1.71054 −0.134822 1.72680i 0.925948 1.00000i 0.230619 + 2.95375i 1.00000i 1.83721 −2.96365 + 0.465620i 1.71054i
1121.14 −1.71054 −0.134822 + 1.72680i 0.925948 1.00000i 0.230619 2.95375i 1.00000i 1.83721 −2.96365 0.465620i 1.71054i
1121.15 −0.805231 −0.972634 + 1.43317i −1.35160 1.00000i 0.783195 1.15404i 1.00000i 2.69881 −1.10797 2.78790i 0.805231i
1121.16 −0.805231 −0.972634 1.43317i −1.35160 1.00000i 0.783195 + 1.15404i 1.00000i 2.69881 −1.10797 + 2.78790i 0.805231i
1121.17 −0.542651 −1.58724 + 0.693309i −1.70553 1.00000i 0.861316 0.376225i 1.00000i 2.01081 2.03865 2.20089i 0.542651i
1121.18 −0.542651 −1.58724 0.693309i −1.70553 1.00000i 0.861316 + 0.376225i 1.00000i 2.01081 2.03865 + 2.20089i 0.542651i
1121.19 0.164753 1.34733 1.08845i −1.97286 1.00000i 0.221976 0.179324i 1.00000i −0.654539 0.630571 2.93298i 0.164753i
1121.20 0.164753 1.34733 + 1.08845i −1.97286 1.00000i 0.221976 + 0.179324i 1.00000i −0.654539 0.630571 + 2.93298i 0.164753i
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.e 40
3.b odd 2 1 1155.2.l.f yes 40
11.b odd 2 1 1155.2.l.f yes 40
33.d even 2 1 inner 1155.2.l.e 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.2.l.e 40 1.a even 1 1 trivial
1155.2.l.e 40 33.d even 2 1 inner
1155.2.l.f yes 40 3.b odd 2 1
1155.2.l.f yes 40 11.b odd 2 1

Hecke kernels

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database