Properties

Label 1224.1.m
Level 1224
Weight 1
Character orbit m
Rep. character \(\chi_{1224}(305,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 2
Sturm bound 216
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1224.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 28 4 24
Cusp forms 12 4 8
Eisenstein series 16 0 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

\( 4q + O(q^{10}) \) \( 4q - 4q^{13} - 4q^{19} + 4q^{43} - 4q^{49} + 4q^{55} + 4q^{85} + O(q^{100}) \)

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.m.a \(2\) \(0.611\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-\beta q^{7}-q^{11}-q^{13}-q^{17}+\cdots\)
1224.1.m.b \(2\) \(0.611\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-\beta q^{7}+q^{11}-q^{13}+q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)

Hecke characteristic polynomials

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