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Properties

Label 1568.2.v
Level $1568$
Weight $2$
Character orbit 1568.v
Rep. character $\chi_{1568}(197,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $636$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 928 676 252
Cusp forms 864 636 228
Eisenstein series 64 40 24

Trace form

\( 636 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 20 q^{8} + 4 q^{9} + O(q^{10}) \) \( 636 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 20 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{16} - 16 q^{18} + 4 q^{19} - 12 q^{20} - 4 q^{23} + 32 q^{24} + 4 q^{25} - 16 q^{26} + 28 q^{27} - 20 q^{29} + 36 q^{30} - 16 q^{31} - 16 q^{32} + 8 q^{33} - 24 q^{34} + 32 q^{36} + 4 q^{37} + 52 q^{38} + 28 q^{39} - 48 q^{40} + 4 q^{41} - 28 q^{43} - 36 q^{44} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 44 q^{50} + 48 q^{51} + 60 q^{52} - 12 q^{53} - 72 q^{54} - 28 q^{55} - 20 q^{57} - 64 q^{58} + 36 q^{59} + 64 q^{60} + 36 q^{61} + 16 q^{64} + 8 q^{65} + 92 q^{66} + 44 q^{67} - 8 q^{68} + 36 q^{69} + 12 q^{71} + 28 q^{72} + 4 q^{73} - 12 q^{74} - 48 q^{75} + 4 q^{76} - 84 q^{78} + 24 q^{80} + 84 q^{82} - 36 q^{83} - 40 q^{85} - 16 q^{86} + 60 q^{87} - 80 q^{88} + 4 q^{89} + 112 q^{90} - 136 q^{92} - 56 q^{93} - 48 q^{94} + 72 q^{95} + 64 q^{96} + 8 q^{97} + 56 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)