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Properties

Label 3584.2.bx
Level $3584$
Weight $2$
Character orbit 3584.bx
Rep. character $\chi_{3584}(47,\cdot)$
Character field $\Q(\zeta_{96})$
Dimension $4032$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.bx (of order \(96\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 896 \)
Character field: \(\Q(\zeta_{96})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3584, [\chi])\).

Total New Old
Modular forms 16640 4160 12480
Cusp forms 16128 4032 12096
Eisenstein series 512 128 384

Trace form

\( 4032 q + 48 q^{3} - 48 q^{5} + 32 q^{7} - 16 q^{9} + O(q^{10}) \) \( 4032 q + 48 q^{3} - 48 q^{5} + 32 q^{7} - 16 q^{9} + 16 q^{11} + 64 q^{15} - 48 q^{17} + 48 q^{19} - 32 q^{21} + 16 q^{23} - 16 q^{25} - 64 q^{29} + 48 q^{31} - 48 q^{33} + 32 q^{35} - 16 q^{37} + 16 q^{39} + 64 q^{43} - 48 q^{45} + 48 q^{47} - 32 q^{49} + 16 q^{51} - 16 q^{53} - 64 q^{57} + 48 q^{59} - 48 q^{61} + 64 q^{63} + 16 q^{67} + 64 q^{71} - 48 q^{73} + 48 q^{75} - 32 q^{77} + 16 q^{79} - 16 q^{81} - 64 q^{85} + 48 q^{87} - 48 q^{89} + 32 q^{91} - 16 q^{93} + 16 q^{95} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)