Properties

Label 1224.1.bv
Level $1224$
Weight $1$
Character orbit 1224.bv
Rep. character $\chi_{1224}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $4$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1224.bv (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 48 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

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

\( 4q + O(q^{10}) \) \( 4q + 4q^{11} - 4q^{16} + 4q^{43} - 4q^{50} + 4q^{59} - 4q^{82} - 4q^{83} - 4q^{88} - 4q^{97} + O(q^{100}) \)

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.bv.a \(4\) \(0.611\) \(\Q(\zeta_{8})\) \(D_{8}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(1-\zeta_{8}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

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