Properties

Label 1155.2.i.d
Level 1155
Weight 2
Character orbit 1155.i
Analytic conductor 9.223
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

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

Newform invariants

Self dual: No
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut -\mathstrut 36q^{4} \) \(\mathstrut -\mathstrut 32q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut -\mathstrut 36q^{4} \) \(\mathstrut -\mathstrut 32q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 32q^{15} \) \(\mathstrut +\mathstrut 44q^{16} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 32q^{25} \) \(\mathstrut +\mathstrut 36q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 52q^{56} \) \(\mathstrut -\mathstrut 48q^{58} \) \(\mathstrut +\mathstrut 36q^{60} \) \(\mathstrut -\mathstrut 156q^{64} \) \(\mathstrut -\mathstrut 72q^{67} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut +\mathstrut 56q^{86} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut +\mathstrut 64q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
76.1 1.26491i 1.00000i 0.399993 1.00000i −1.26491 0.0556365 2.64517i 3.03578i −1.00000 −1.26491
76.2 1.26491i 1.00000i 0.399993 1.00000i −1.26491 0.0556365 + 2.64517i 3.03578i −1.00000 −1.26491
76.3 0.370647i 1.00000i 1.86262 1.00000i −0.370647 −2.39596 + 1.12222i 1.43167i −1.00000 −0.370647
76.4 0.370647i 1.00000i 1.86262 1.00000i −0.370647 −2.39596 1.12222i 1.43167i −1.00000 −0.370647
76.5 2.40558i 1.00000i −3.78682 1.00000i −2.40558 1.69010 2.03557i 4.29833i −1.00000 −2.40558
76.6 2.40558i 1.00000i −3.78682 1.00000i −2.40558 1.69010 + 2.03557i 4.29833i −1.00000 −2.40558
76.7 2.76869i 1.00000i −5.66565 1.00000i −2.76869 −2.02228 1.70599i 10.1491i −1.00000 −2.76869
76.8 2.76869i 1.00000i −5.66565 1.00000i −2.76869 −2.02228 + 1.70599i 10.1491i −1.00000 −2.76869
76.9 0.859876i 1.00000i 1.26061 1.00000i 0.859876 −2.42783 1.05149i 2.80372i −1.00000 0.859876
76.10 0.859876i 1.00000i 1.26061 1.00000i 0.859876 −2.42783 + 1.05149i 2.80372i −1.00000 0.859876
76.11 1.29033i 1.00000i 0.335051 1.00000i −1.29033 2.23077 + 1.42256i 3.01298i −1.00000 −1.29033
76.12 1.29033i 1.00000i 0.335051 1.00000i −1.29033 2.23077 1.42256i 3.01298i −1.00000 −1.29033
76.13 1.54704i 1.00000i −0.393347 1.00000i −1.54704 −2.51711 0.814965i 2.48556i −1.00000 −1.54704
76.14 1.54704i 1.00000i −0.393347 1.00000i −1.54704 −2.51711 + 0.814965i 2.48556i −1.00000 −1.54704
76.15 2.23885i 1.00000i −3.01246 1.00000i −2.23885 −0.322004 + 2.62608i 2.26674i −1.00000 −2.23885
76.16 2.23885i 1.00000i −3.01246 1.00000i −2.23885 −0.322004 2.62608i 2.26674i −1.00000 −2.23885
76.17 2.23885i 1.00000i −3.01246 1.00000i 2.23885 0.322004 + 2.62608i 2.26674i −1.00000 2.23885
76.18 2.23885i 1.00000i −3.01246 1.00000i 2.23885 0.322004 2.62608i 2.26674i −1.00000 2.23885
76.19 1.54704i 1.00000i −0.393347 1.00000i 1.54704 2.51711 0.814965i 2.48556i −1.00000 1.54704
76.20 1.54704i 1.00000i −0.393347 1.00000i 1.54704 2.51711 + 0.814965i 2.48556i −1.00000 1.54704
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 76.32
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{16} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(1155, [\chi])\).