Properties

Label 3584.2.i
Level $3584$
Weight $2$
Character orbit 3584.i
Rep. character $\chi_{3584}(513,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $256$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 1088 256 832
Cusp forms 960 256 704
Eisenstein series 128 0 128

Trace form

\( 256 q - 128 q^{9} + O(q^{10}) \) \( 256 q - 128 q^{9} - 128 q^{25} - 128 q^{81} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)