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Properties

Label 1200.2.bf
Level $1200$
Weight $2$
Character orbit 1200.bf
Rep. character $\chi_{1200}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.bf (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

Trace form

\( 280 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + O(q^{10}) \) \( 280 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{12} + 8 q^{13} + 12 q^{18} - 16 q^{19} - 4 q^{21} + 4 q^{22} + 12 q^{24} + 4 q^{27} + 4 q^{28} - 16 q^{31} + 4 q^{33} + 56 q^{34} - 20 q^{36} + 8 q^{37} - 24 q^{39} - 40 q^{42} + 48 q^{46} - 32 q^{48} - 4 q^{51} + 48 q^{52} - 24 q^{54} + 12 q^{57} + 20 q^{58} + 24 q^{61} + 32 q^{63} - 56 q^{64} - 36 q^{66} + 12 q^{69} - 24 q^{72} + 48 q^{76} - 60 q^{78} - 8 q^{81} - 64 q^{82} + 60 q^{84} - 12 q^{87} - 44 q^{88} - 8 q^{91} + 16 q^{93} - 40 q^{94} - 108 q^{96} + 8 q^{97} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)