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Properties

Label 3528.2.ds
Level $3528$
Weight $2$
Character orbit 3528.ds
Rep. character $\chi_{3528}(193,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2016$
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.ds (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8160 2016 6144
Cusp forms 7968 2016 5952
Eisenstein series 192 0 192

Trace form

\( 2016 q + 8 q^{5} - 26 q^{9} + O(q^{10}) \) \( 2016 q + 8 q^{5} - 26 q^{9} - 8 q^{17} - 18 q^{21} - 336 q^{25} + 6 q^{27} + 48 q^{29} - 6 q^{31} + 4 q^{33} - 12 q^{35} - 12 q^{39} - 18 q^{41} - 6 q^{43} + 34 q^{45} + 78 q^{47} - 12 q^{49} + 6 q^{51} - 4 q^{53} + 30 q^{55} + 8 q^{57} + 36 q^{59} - 6 q^{61} + 4 q^{63} - 52 q^{69} + 16 q^{71} - 60 q^{75} - 4 q^{77} + 6 q^{79} + 110 q^{81} + 36 q^{83} + 10 q^{87} - 18 q^{89} + 6 q^{91} - 132 q^{93} + 18 q^{95} + 36 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)