Properties

Label 3744.1.o
Level 3744
Weight 1
Character orbit o
Rep. character \(\chi_{3744}(2287,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 3
Sturm bound 672
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3744.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(672\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3744, [\chi])\).

Total New Old
Modular forms 80 8 72
Cusp forms 48 6 42
Eisenstein series 32 2 30

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + O(q^{10}) \) \( 6q + 2q^{17} + 4q^{25} + 2q^{35} - 6q^{43} - 4q^{49} + 2q^{65} + 2q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3744.1.o.a \(1\) \(1.868\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}-q^{13}+q^{17}+2q^{31}+\cdots\)
3744.1.o.b \(1\) \(1.868\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{13}+q^{17}-2q^{31}+\cdots\)
3744.1.o.c \(4\) \(1.868\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

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