Properties

Label 2016.1.cd
Level $2016$
Weight $1$
Character orbit 2016.cd
Rep. character $\chi_{2016}(415,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2016.cd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2016, [\chi])\).

Total New Old
Modular forms 88 4 84
Cusp forms 24 4 20
Eisenstein series 64 0 64

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4 q + 2 q^{5} + O(q^{10}) \) \( 4 q + 2 q^{5} + 2 q^{17} + 2 q^{37} - 4 q^{49} - 2 q^{53} + 2 q^{61} + 2 q^{73} - 2 q^{77} + 4 q^{85} - 2 q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2016.1.cd.a 2016.cd 28.g $4$ $1.006$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)