Properties

Label 3528.1.bp
Level $3528$
Weight $1$
Character orbit 3528.bp
Rep. character $\chi_{3528}(1501,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $3$
Sturm bound $672$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.bp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(672\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3528, [\chi])\).

Total New Old
Modular forms 40 24 16
Cusp forms 8 8 0
Eisenstein series 32 16 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} + 8 q^{15} + 8 q^{16} - 4 q^{18} + 4 q^{23} - 4 q^{25} - 4 q^{30} + 8 q^{39} + 4 q^{50} - 4 q^{57} + 8 q^{60} + 8 q^{64} - 8 q^{65} - 4 q^{72} + 8 q^{78} - 4 q^{81} + 4 q^{92} + 16 q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3528.1.bp.a 3528.bp 504.ap $2$ $1.761$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-14}) \) None \(2\) \(-1\) \(1\) \(0\) \(q+q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{6}+\cdots\)
3528.1.bp.b 3528.bp 504.ap $2$ $1.761$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-14}) \) None \(2\) \(1\) \(-1\) \(0\) \(q+q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
3528.1.bp.c 3528.bp 504.ap $4$ $1.761$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-14}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{12}q^{3}+q^{4}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)