Properties

Label 2013.1.bm
Level 2013
Weight 1
Character orbit bm
Rep. character \(\chi_{2013}(548,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 32
Newform subspaces 4
Sturm bound 248
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2013.bm (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2013 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(248\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2013, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 32 32 0
Eisenstein series 16 16 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32q - 8q^{4} - 8q^{9} + O(q^{10}) \) \( 32q - 8q^{4} - 8q^{9} - 8q^{16} - 8q^{25} - 8q^{36} - 16q^{46} - 16q^{48} - 8q^{49} - 16q^{52} + 24q^{58} - 8q^{64} - 8q^{66} + 64q^{76} - 8q^{81} - 8q^{88} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2013, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2013.1.bm.a \(4\) \(1.005\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-183}) \) None \(-3\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
2013.1.bm.b \(4\) \(1.005\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-183}) \) None \(3\) \(-1\) \(0\) \(0\) \(q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
2013.1.bm.c \(8\) \(1.005\) \(\Q(\zeta_{20})\) \(D_{10}\) \(\Q(\sqrt{-183}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2013.1.bm.d \(16\) \(1.005\) \(\Q(\zeta_{40})\) \(D_{20}\) \(\Q(\sqrt{-183}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T )^{4}( 1 - T + T^{2} - T^{3} + T^{4} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))(\( ( 1 + T^{4} )^{4}( 1 - T^{4} + T^{8} - T^{12} + T^{16} ) \))
$3$ (\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4} \))
$5$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$7$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$11$ (\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} \))
$13$ (\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T )^{8}( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T^{2} )^{8}( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$17$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{2} \))
$19$ (\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T )^{8}( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T^{2} )^{8}( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$23$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{2} \))
$29$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{2} \))
$31$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$37$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$41$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$43$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{8}( 1 + T )^{8} \))(\( ( 1 - T )^{16}( 1 + T )^{16} \))
$47$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$53$ (\( ( 1 + T )^{4}( 1 - T + T^{2} - T^{3} + T^{4} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))(\( ( 1 + T^{4} )^{4}( 1 - T^{4} + T^{8} - T^{12} + T^{16} ) \))
$59$ (\( ( 1 + T )^{4}( 1 - T + T^{2} - T^{3} + T^{4} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))(\( ( 1 + T^{4} )^{4}( 1 - T^{4} + T^{8} - T^{12} + T^{16} ) \))
$61$ (\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4} \))
$67$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{8}( 1 + T )^{8} \))(\( ( 1 - T )^{16}( 1 + T )^{16} \))
$71$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{2} \))
$73$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{8} \))
$79$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$83$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$89$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} )^{2} \))
$97$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{4} \))
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