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Properties

Label 3584.2.bk
Level $3584$
Weight $2$
Character orbit 3584.bk
Rep. character $\chi_{3584}(111,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $2016$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.bk (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 896 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 8320 2080 6240
Cusp forms 8064 2016 6048
Eisenstein series 256 64 192

Trace form

\( 2016 q + 16 q^{7} - 32 q^{9} + O(q^{10}) \) \( 2016 q + 16 q^{7} - 32 q^{9} + 32 q^{11} + 32 q^{15} - 16 q^{21} + 32 q^{23} - 32 q^{25} - 32 q^{29} + 16 q^{35} - 32 q^{37} + 32 q^{39} + 32 q^{43} - 16 q^{49} + 32 q^{51} - 32 q^{53} - 32 q^{57} + 32 q^{63} + 32 q^{67} + 32 q^{71} - 16 q^{77} + 32 q^{79} - 32 q^{81} - 32 q^{85} + 16 q^{91} - 32 q^{93} + 32 q^{95} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \)