Properties

Label 1224.1.cb
Level $1224$
Weight $1$
Character orbit 1224.cb
Rep. character $\chi_{1224}(115,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $8$
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.cb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1224 \)
Character field: \(\Q(\zeta_{12})\)
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 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

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

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

Trace form

\( 8q + 2q^{3} + 4q^{4} + 2q^{6} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{4} + 2q^{6} + 2q^{11} + 4q^{12} - 4q^{16} - 2q^{22} - 2q^{24} - 4q^{27} + 4q^{33} - 2q^{34} + 4q^{38} - 2q^{41} + 4q^{44} + 2q^{48} - 4q^{50} - 4q^{51} - 2q^{54} + 2q^{57} - 8q^{64} + 4q^{73} - 2q^{75} - 4q^{81} - 4q^{82} + 2q^{88} - 4q^{96} + 2q^{97} - 8q^{98} + O(q^{100}) \)

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.cb.a \(4\) \(0.611\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
1224.1.cb.b \(4\) \(0.611\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots\)

Hecke characteristic polynomials

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