Properties

Label 2016.1.l
Level $2016$
Weight $1$
Character orbit 2016.l
Rep. character $\chi_{2016}(433,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2016.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 56 5 51
Cusp forms 24 3 21
Eisenstein series 32 2 30

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q - q^{7} + O(q^{10}) \) \( 3 q - q^{7} + 2 q^{23} - 3 q^{25} + 3 q^{49} - 2 q^{71} + 6 q^{79} + O(q^{100}) \)

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.l.a 2016.l 56.h $1$ $1.006$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots\)
2016.1.l.b 2016.l 56.h $2$ $1.006$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)