Properties

Label 2016.1.dp
Level $2016$
Weight $1$
Character orbit 2016.dp
Rep. character $\chi_{2016}(181,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $12$
Newform subspaces $3$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2016.dp (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 56 20 36
Cusp forms 24 12 12
Eisenstein series 32 8 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + O(q^{10}) \) \( 12 q - 12 q^{16} - 4 q^{22} + 4 q^{23} + 4 q^{43} - 4 q^{44} + 4 q^{53} - 4 q^{56} + 12 q^{67} - 4 q^{74} + 4 q^{77} + 4 q^{92} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2016.1.dp.a $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
2016.1.dp.b $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}q^{8}+\cdots\)
2016.1.dp.c $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)

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

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