Properties

Label 1224.1.s
Level $1224$
Weight $1$
Character orbit 1224.s
Rep. character $\chi_{1224}(523,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(i)\)
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 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{4} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{11} + 2q^{16} - 2q^{22} - 2q^{34} - 4q^{38} + 2q^{41} + 2q^{44} - 2q^{50} - 2q^{64} - 2q^{73} + 2q^{82} + 2q^{88} + 2q^{97} + 2q^{98} + O(q^{100}) \)

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.s.a \(2\) \(0.611\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+(-1-i)q^{11}+\cdots\)

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

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