Properties

Label 2880.1.bh
Level 2880
Weight 1
Character orbit bh
Rep. character \(\chi_{2880}(577,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 6
Newform subspaces 3
Sturm bound 576
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2880.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(576\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2880, [\chi])\).

Total New Old
Modular forms 132 10 122
Cusp forms 36 6 30
Eisenstein series 96 4 92

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

\( 6q + O(q^{10}) \) \( 6q - 2q^{13} + 2q^{17} + 2q^{25} - 6q^{37} + 2q^{53} - 2q^{65} - 2q^{73} + 6q^{85} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2880.1.bh.a \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}+(-1-i)q^{13}+(-1+i)q^{17}+\cdots\)
2880.1.bh.b \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+(1+i)q^{13}+(1-i)q^{17}-q^{25}+\cdots\)
2880.1.bh.c \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}+(-1-i)q^{13}+(1-i)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

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