Properties

Label 3528.1.cu
Level $3528$
Weight $1$
Character orbit 3528.cu
Rep. character $\chi_{3528}(1745,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.cu (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 180 4 176
Cusp forms 52 4 48
Eisenstein series 128 0 128

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

\( 4q + O(q^{10}) \) \( 4q + 4q^{13} - 2q^{19} + 2q^{25} - 2q^{31} - 2q^{37} - 4q^{43} + 8q^{55} + 2q^{67} + 2q^{73} - 2q^{79} + O(q^{100}) \)

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.cu.a \(4\) \(1.761\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}+q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)