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Properties

Label 3200.2.ba
Level $3200$
Weight $2$
Character orbit 3200.ba
Rep. character $\chi_{3200}(49,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $280$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.ba (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3200, [\chi])\).

Total New Old
Modular forms 2016 296 1720
Cusp forms 1824 280 1544
Eisenstein series 192 16 176

Trace form

\( 280 q + 8 q^{9} + O(q^{10}) \) \( 280 q + 8 q^{9} + 8 q^{11} - 8 q^{19} - 8 q^{21} + 8 q^{29} - 32 q^{31} - 8 q^{39} - 8 q^{41} - 48 q^{51} + 56 q^{59} - 72 q^{61} + 72 q^{69} - 56 q^{71} + 8 q^{89} + 8 q^{91} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)