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Properties

Label 3600.1.bb
Level $3600$
Weight $1$
Character orbit 3600.bb
Rep. character $\chi_{3600}(757,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $720$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3600.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(720\)
Trace bound: \(17\)

Dimensions

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

Total New Old
Modular forms 52 8 44
Cusp forms 4 4 0
Eisenstein series 48 4 44

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

\( 4q - 4q^{4} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{16} - 4q^{19} + 4q^{34} + 4q^{46} + 4q^{61} - 4q^{64} + 4q^{76} + 4q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bb.a \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+(-1+i+\cdots)q^{17}+\cdots\)
3600.1.bb.b \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+q^{16}+(1-i+\cdots)q^{17}+\cdots\)

Hecke characteristic polynomials

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