Properties

Label 3600.1.l
Level 3600
Weight 1
Character orbit l
Rep. character \(\chi_{3600}(1601,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 2
Sturm bound 720
Trace bound 7

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3600.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(720\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 100 4 96
Cusp forms 28 4 24
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 0 0 4 0

Trace form

\( 4q + O(q^{10}) \) \( 4q - 4q^{19} - 4q^{31} + 4q^{61} + 4q^{91} + O(q^{100}) \)

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.l.a \(2\) \(1.797\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+\beta q^{11}-q^{13}-\beta q^{17}-q^{19}+\cdots\)
3600.1.l.b \(2\) \(1.797\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\beta q^{11}+q^{13}-\beta q^{17}-q^{19}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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