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Properties

Label 1584.2.bn
Level $1584$
Weight $2$
Character orbit 1584.bn
Rep. character $\chi_{1584}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $140$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

Total New Old
Modular forms 600 148 452
Cusp forms 552 140 412
Eisenstein series 48 8 40

Trace form

\( 140 q + 4 q^{3} - 6 q^{5} - 8 q^{9} + O(q^{10}) \) \( 140 q + 4 q^{3} - 6 q^{5} - 8 q^{9} + 3 q^{11} + 4 q^{15} + 6 q^{23} + 60 q^{25} + 16 q^{27} + 2 q^{31} - 7 q^{33} - 8 q^{37} - 14 q^{45} + 24 q^{47} + 56 q^{49} + 14 q^{55} + 6 q^{59} + 2 q^{67} - 42 q^{69} + 2 q^{75} - 27 q^{77} + 36 q^{91} + 18 q^{93} - 14 q^{97} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)