Properties

Label 1161.1.i
Level 1161
Weight 1
Character orbit i
Rep. character \(\chi_{1161}(350,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 14
Newforms 3
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1161 = 3^{3} \cdot 43 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1161.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 129 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
Sturm bound: \(132\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1161, [\chi])\).

Total New Old
Modular forms 26 14 12
Cusp forms 14 14 0
Eisenstein series 12 0 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 4 8

Trace form

\(14q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut -\mathstrut 10q^{16} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 3q^{25} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 3q^{52} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 3q^{76} \) \(\mathstrut -\mathstrut 3q^{79} \) \(\mathstrut +\mathstrut 12q^{82} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1161, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1161.1.i.a \(2\) \(0.579\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+q^{4}-\zeta_{6}q^{7}+\zeta_{6}q^{13}+q^{16}-\zeta_{6}^{2}q^{19}+\cdots\)
1161.1.i.b \(4\) \(0.579\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{5}+(-2+2\beta _{2}+\cdots)q^{10}+\cdots\)
1161.1.i.c \(8\) \(0.579\) 8.0.12960000.1 \(A_{5}\) None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)