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Properties

Label 3528.2.bs
Level $3528$
Weight $2$
Character orbit 3528.bs
Rep. character $\chi_{3528}(2273,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

Total New Old
Modular forms 1408 240 1168
Cusp forms 1280 240 1040
Eisenstein series 128 0 128

Trace form

\( 240 q + 4 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{9} - 16 q^{15} + 24 q^{23} - 120 q^{25} + 18 q^{27} - 18 q^{29} + 14 q^{39} - 6 q^{41} + 6 q^{43} - 6 q^{45} - 36 q^{47} + 36 q^{51} - 12 q^{53} - 16 q^{57} + 54 q^{75} + 12 q^{79} - 20 q^{81} + 24 q^{87} - 18 q^{89} - 8 q^{93} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)