Properties

Label 3200.2.ci
Level $3200$
Weight $2$
Character orbit 3200.ci
Rep. character $\chi_{3200}(149,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $4576$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.ci (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 640 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7776 4640 3136
Cusp forms 7584 4576 3008
Eisenstein series 192 64 128

Trace form

\( 4576 q + 32 q^{4} - 32 q^{6} + 32 q^{9} + O(q^{10}) \) \( 4576 q + 32 q^{4} - 32 q^{6} + 32 q^{9} - 32 q^{11} + 32 q^{14} - 32 q^{16} + 32 q^{19} - 32 q^{21} + 32 q^{24} - 32 q^{26} + 32 q^{29} - 32 q^{31} + 32 q^{34} - 32 q^{36} + 32 q^{39} - 32 q^{41} + 32 q^{44} - 32 q^{46} + 32 q^{49} - 32 q^{51} + 288 q^{54} + 64 q^{56} + 32 q^{59} - 32 q^{61} + 416 q^{64} - 416 q^{66} + 32 q^{69} - 32 q^{71} - 64 q^{74} - 288 q^{76} + 32 q^{79} - 32 q^{81} + 32 q^{84} - 32 q^{86} + 32 q^{89} - 32 q^{91} + 32 q^{94} - 32 q^{96} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)