Properties

Label 3600.1.cc
Level $3600$
Weight $1$
Character orbit 3600.cc
Rep. character $\chi_{3600}(751,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $720$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3600.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(720\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).

Total New Old
Modular forms 88 4 84
Cusp forms 16 4 12
Eisenstein series 72 0 72

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

\( 4q - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{9} - 2q^{29} - 2q^{41} + 4q^{49} - 2q^{61} + 6q^{69} - 2q^{81} + 4q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3600.1.cc.a \(2\) \(1.797\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-5}) \) None \(0\) \(-1\) \(0\) \(-3\) \(q-\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3600.1.cc.b \(2\) \(1.797\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-5}) \) None \(0\) \(1\) \(0\) \(3\) \(q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

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