Properties

Label 1224.1.bu
Level $1224$
Weight $1$
Character orbit 1224.bu
Rep. character $\chi_{1224}(53,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $8$
Newform subspaces $2$
Sturm bound $216$
Trace bound $14$

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.bu (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 408 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(14\)

Dimensions

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

Total New Old
Modular forms 40 8 32
Cusp forms 8 8 0
Eisenstein series 32 0 32

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

\( 8q + 8q^{7} + O(q^{10}) \) \( 8q + 8q^{7} - 8q^{16} + 8q^{49} - 8q^{79} - 8q^{94} + O(q^{100}) \)

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.bu.a \(4\) \(0.611\) \(\Q(\zeta_{8})\) \(D_{8}\) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3})q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
1224.1.bu.b \(4\) \(0.611\) \(\Q(\zeta_{8})\) \(D_{8}\) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3})q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)

Hecke characteristic polynomials

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