Properties

Label 1224.1.bb
Level $1224$
Weight $1$
Character orbit 1224.bb
Rep. character $\chi_{1224}(67,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $216$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1224.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1224 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1224, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

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

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

Trace form

\( 4q + 2q^{2} - 2q^{4} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{8} - 2q^{9} - 2q^{16} + 2q^{17} - 4q^{18} + 4q^{19} + 2q^{25} + 2q^{32} - 6q^{33} + q^{34} - 2q^{36} + 2q^{38} + 2q^{43} + 2q^{49} - 2q^{50} + 3q^{51} + 2q^{59} + 4q^{64} - 2q^{67} - q^{68} + 2q^{72} - 2q^{76} - 2q^{81} - 4q^{83} - 2q^{86} - 8q^{89} + 4q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1224.1.bb.a \(2\) \(0.611\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
1224.1.bb.b \(2\) \(0.611\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)

Hecke characteristic polynomials

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