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Properties

Label 1584.2.cm
Level $1584$
Weight $2$
Character orbit 1584.cm
Rep. character $\chi_{1584}(49,\cdot)$
Character field $\Q(\zeta_{15})$
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.cm (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 560 q + 6 q^{3} - 3 q^{5} + 3 q^{7} - 2 q^{9} + O(q^{10}) \) \( 560 q + 6 q^{3} - 3 q^{5} + 3 q^{7} - 2 q^{9} + 4 q^{11} - 3 q^{13} + 6 q^{15} - 4 q^{17} + 12 q^{19} - 22 q^{21} + 8 q^{23} + 59 q^{25} + 18 q^{27} - 3 q^{29} + 3 q^{31} - 15 q^{33} + 80 q^{35} - 12 q^{37} - 60 q^{39} + q^{41} + 8 q^{43} - 26 q^{45} + 9 q^{47} + 55 q^{49} + 30 q^{51} - 12 q^{53} + 26 q^{55} + 14 q^{57} + 3 q^{59} - 3 q^{61} + 20 q^{63} - 28 q^{65} + 8 q^{67} - 29 q^{69} - 36 q^{71} + 12 q^{73} + 16 q^{75} - 26 q^{77} + 3 q^{79} - 10 q^{81} - 33 q^{83} + 7 q^{85} - 14 q^{87} - 48 q^{89} + 40 q^{91} + 4 q^{93} + 25 q^{95} + 15 q^{97} + 57 q^{99} + O(q^{100}) \)

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

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