Properties

Label 3600.1.c
Level 3600
Weight 1
Character orbit c
Rep. character \(\chi_{3600}(449,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 720
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3600.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(720\)
Trace bound: \(0\)

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.c.a \(4\) \(1.797\) \(\Q(\zeta_{8})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\zeta_{8}^{2}q^{13}+\cdots\)

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