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Properties

Label 1584.2.cw
Level $1584$
Weight $2$
Character orbit 1584.cw
Rep. character $\chi_{1584}(497,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $560$
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.cw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2400 592 1808
Cusp forms 2208 560 1648
Eisenstein series 192 32 160

Trace form

\( 560 q + 6 q^{3} - 9 q^{5} + 5 q^{7} - 2 q^{9} + O(q^{10}) \) \( 560 q + 6 q^{3} - 9 q^{5} + 5 q^{7} - 2 q^{9} + 12 q^{11} - 5 q^{13} + 6 q^{15} + 20 q^{19} + 24 q^{23} - 65 q^{25} - 6 q^{27} - 15 q^{29} + 3 q^{31} + 7 q^{33} - 12 q^{37} + 130 q^{39} - 15 q^{41} - 6 q^{45} - 9 q^{47} - 61 q^{49} - 50 q^{51} + 6 q^{55} - 30 q^{57} + 9 q^{59} - 5 q^{61} + 10 q^{63} + 8 q^{67} + 17 q^{69} - 20 q^{73} + 8 q^{75} + 12 q^{77} + 5 q^{79} - 10 q^{81} + 15 q^{83} - 5 q^{85} - 16 q^{91} - 28 q^{93} + 15 q^{95} - 21 q^{97} + 39 q^{99} + O(q^{100}) \)

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

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