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Properties

Label 3528.1.bw
Level $3528$
Weight $1$
Character orbit 3528.bw
Rep. character $\chi_{3528}(325,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $3$
Sturm bound $672$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(672\)
Trace bound: \(10\)

Dimensions

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

Total New Old
Modular forms 88 18 70
Cusp forms 24 10 14
Eisenstein series 64 8 56

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q - q^{2} + 3 q^{4} + 2 q^{8} + O(q^{10}) \) \( 10 q - q^{2} + 3 q^{4} + 2 q^{8} + 6 q^{10} - 5 q^{16} - 4 q^{22} + 2 q^{23} - q^{25} - 6 q^{31} - q^{32} + 6 q^{40} + 2 q^{46} - 2 q^{50} - 2 q^{58} - 6 q^{64} + 4 q^{71} + 4 q^{79} - 2 q^{88} - 4 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bw.a 3528.bw 56.j $2$ $1.761$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
3528.1.bw.b 3528.bw 56.j $4$ $1.761$ \(\Q(\zeta_{12})\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots\)
3528.1.bw.c 3528.bw 56.j $4$ $1.761$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \)