Properties

Label 3528.1.bx
Level $3528$
Weight $1$
Character orbit 3528.bx
Rep. character $\chi_{3528}(667,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $3$
Sturm bound $672$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.bx (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: \(2\)

Dimensions

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

Total New Old
Modular forms 92 18 74
Cusp forms 28 10 18
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

\( 10q - q^{2} - q^{4} + 2q^{8} + O(q^{10}) \) \( 10q - q^{2} - q^{4} + 2q^{8} - 2q^{11} - 5q^{16} - 4q^{22} - 5q^{25} - q^{32} + 4q^{43} - 2q^{44} + 4q^{46} + 2q^{50} - 4q^{58} + 2q^{64} - 2q^{67} - 2q^{86} + 2q^{88} + O(q^{100}) \)

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.bx.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots\)
3528.1.bx.b \(4\) \(1.761\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+q^{8}+\beta _{2}q^{16}+\cdots\)
3528.1.bx.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{4}q^{16}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)