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
Newform subspaces 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: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(1161, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(0\) \(2\) \(q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$3$ 1
$5$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( 1 - T^{4} + T^{8} \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$7$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2} \))
$11$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$13$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2} \))
$17$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$19$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2} \))
$23$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( 1 - T^{4} + T^{8} \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$29$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4} \))
$31$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$37$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$41$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$43$ (\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T + T^{2} )^{4} \))
$47$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{8}( 1 + T )^{8} \))
$53$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( 1 - T^{4} + T^{8} \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$59$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$61$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T )^{8}( 1 - T + T^{2} )^{4} \))
$67$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 + T )^{8}( 1 - T + T^{2} )^{4} \))
$71$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \))
$73$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$79$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 + T - T^{3} - T^{4} - T^{5} + T^{7} + T^{8} )^{2} \))
$83$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \))
$89$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4} \))
$97$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4} \))
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