Properties

Label 1224.1.n
Level $1224$
Weight $1$
Character orbit 1224.n
Rep. character $\chi_{1224}(883,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $216$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 16 7 9
Cusp forms 8 5 3
Eisenstein series 8 2 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5q + q^{2} + 5q^{4} + q^{8} + O(q^{10}) \) \( 5q + q^{2} + 5q^{4} + q^{8} + 5q^{16} + q^{17} - 2q^{19} + 3q^{25} + q^{32} - 3q^{34} - 2q^{38} - 6q^{43} + 3q^{49} - q^{50} - 2q^{59} + 5q^{64} - 2q^{67} + q^{68} - 8q^{70} - 2q^{76} - 2q^{83} + 2q^{86} + 2q^{89} - q^{98} + O(q^{100}) \)

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.n.a \(1\) \(0.611\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}+q^{17}-2q^{19}+\cdots\)
1224.1.n.b \(2\) \(0.611\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-34}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots\)
1224.1.n.c \(2\) \(0.611\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{5}+\beta q^{7}+q^{8}-\beta q^{10}+\cdots\)

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

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