Properties

Label 1584.2.q
Level $1584$
Weight $2$
Character orbit 1584.q
Rep. character $\chi_{1584}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $120$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 600 120 480
Cusp forms 552 120 432
Eisenstein series 48 0 48

Trace form

\( 120 q + O(q^{10}) \) \( 120 q - 6 q^{11} - 6 q^{15} + 8 q^{21} + 12 q^{23} - 60 q^{25} + 24 q^{27} - 8 q^{29} - 12 q^{31} + 12 q^{39} - 12 q^{43} - 16 q^{45} + 26 q^{47} - 60 q^{49} + 20 q^{51} + 16 q^{57} - 48 q^{59} - 76 q^{63} - 16 q^{65} + 8 q^{69} - 56 q^{71} - 98 q^{75} - 40 q^{81} - 20 q^{83} + 4 q^{87} - 16 q^{89} + 24 q^{91} - 24 q^{93} + 36 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)