Properties

Label 3528.1.bi
Level $3528$
Weight $1$
Character orbit 3528.bi
Rep. character $\chi_{3528}(1157,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $672$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(672\)
Trace bound: \(0\)

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

\( 8q - 8q^{4} + O(q^{10}) \) \( 8q - 8q^{4} - 8q^{15} + 8q^{16} - 4q^{18} + 12q^{23} - 4q^{25} + 4q^{30} - 8q^{39} + 12q^{50} + 4q^{57} + 8q^{60} - 8q^{64} + 4q^{72} + 8q^{78} + 4q^{81} - 12q^{92} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3528.1.bi.a \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}-\zeta_{24}^{7}q^{3}-q^{4}+(-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)