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Properties

Label 2013.1.bm
Level $2013$
Weight $1$
Character orbit 2013.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2013.1.bm.a 2013.bm 2013.am $4$ $1.005$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-183}) \) 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 2013.bm 2013.am $4$ $1.005$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-183}) \) 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 2013.bm 2013.am $8$ $1.005$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-183}) \) 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 2013.bm 2013.am $16$ $1.005$ \(\Q(\zeta_{40})\) $D_{20}$ \(\Q(\sqrt{-183}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots\)