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Properties

Label 1568.2.bm
Level $1568$
Weight $2$
Character orbit 1568.bm
Rep. character $\chi_{1568}(165,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1248$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.bm (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1568, [\chi])\).

Total New Old
Modular forms 1856 1312 544
Cusp forms 1728 1248 480
Eisenstein series 128 64 64

Trace form

\( 1248 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 16 q^{6} - 32 q^{8} + 4 q^{9} + O(q^{10}) \) \( 1248 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 16 q^{6} - 32 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 44 q^{16} + 44 q^{18} + 4 q^{19} + 48 q^{20} - 16 q^{22} + 20 q^{23} - 36 q^{24} + 4 q^{25} + 4 q^{26} + 16 q^{27} - 32 q^{29} - 84 q^{30} + 56 q^{31} + 4 q^{32} + 8 q^{33} + 32 q^{34} + 128 q^{36} + 4 q^{37} - 36 q^{38} + 4 q^{39} + 68 q^{40} + 16 q^{41} - 64 q^{43} - 48 q^{44} - 8 q^{45} + 4 q^{46} + 16 q^{48} - 56 q^{50} - 44 q^{51} + 28 q^{52} + 36 q^{53} + 92 q^{54} + 16 q^{55} - 32 q^{57} - 28 q^{58} + 36 q^{59} - 108 q^{60} + 4 q^{61} - 104 q^{64} + 8 q^{65} + 36 q^{66} - 76 q^{67} + 36 q^{68} + 16 q^{69} - 96 q^{71} + 4 q^{72} + 4 q^{73} - 96 q^{74} - 16 q^{75} + 16 q^{76} + 72 q^{78} + 16 q^{80} + 44 q^{82} + 96 q^{83} + 8 q^{85} + 4 q^{86} + 4 q^{87} - 40 q^{88} + 4 q^{89} - 224 q^{90} + 24 q^{92} + 52 q^{93} - 4 q^{94} + 8 q^{95} + 32 q^{96} + 32 q^{97} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)