Properties

Label 1224.1.cp
Level $1224$
Weight $1$
Character orbit 1224.cp
Rep. character $\chi_{1224}(43,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $16$
Newform subspaces $2$
Sturm bound $216$
Trace bound $9$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1224.cp (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1224 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(9\)

Dimensions

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

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q + 4q^{9} + O(q^{10}) \) \( 16q + 4q^{9} - 4q^{11} + 8q^{12} + 8q^{16} - 4q^{24} + 4q^{36} + 4q^{43} - 8q^{50} - 4q^{54} - 12q^{57} - 4q^{59} - 4q^{66} + 4q^{75} + 8q^{82} - 8q^{83} - 4q^{88} - 4q^{97} - 4q^{99} + O(q^{100}) \)

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.cp.a \(8\) \(0.611\) \(\Q(\zeta_{24})\) \(D_{24}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{2}q^{6}+\cdots\)
1224.1.cp.b \(8\) \(0.611\) \(\Q(\zeta_{24})\) \(D_{24}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-\zeta_{24}^{10}q^{3}+\zeta_{24}^{2}q^{4}+\cdots\)

Hecke characteristic polynomials

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