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Properties

Label 1568.2.ck
Level $1568$
Weight $2$
Character orbit 1568.ck
Rep. character $\chi_{1568}(37,\cdot)$
Character field $\Q(\zeta_{168})$
Dimension $10656$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.ck (of order \(168\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1568 \)
Character field: \(\Q(\zeta_{168})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 10848 10848 0
Cusp forms 10656 10656 0
Eisenstein series 192 192 0

Trace form

\( 10656 q - 52 q^{2} - 52 q^{3} - 52 q^{4} - 52 q^{5} - 40 q^{6} - 48 q^{7} - 40 q^{8} - 52 q^{9} + O(q^{10}) \) \( 10656 q - 52 q^{2} - 52 q^{3} - 52 q^{4} - 52 q^{5} - 40 q^{6} - 48 q^{7} - 40 q^{8} - 52 q^{9} - 52 q^{10} - 52 q^{11} - 52 q^{12} - 40 q^{13} - 80 q^{14} - 52 q^{16} - 24 q^{18} - 24 q^{19} - 8 q^{20} - 48 q^{21} - 40 q^{22} - 52 q^{23} - 92 q^{24} - 52 q^{25} - 52 q^{26} - 40 q^{27} - 68 q^{28} - 40 q^{29} - 32 q^{30} - 336 q^{31} - 52 q^{32} - 104 q^{33} - 24 q^{34} - 24 q^{35} - 40 q^{36} - 52 q^{37} - 92 q^{38} - 52 q^{39} - 212 q^{40} - 40 q^{41} - 28 q^{42} - 40 q^{43} - 96 q^{44} - 64 q^{45} - 52 q^{46} - 96 q^{48} - 120 q^{50} - 28 q^{51} - 28 q^{52} - 52 q^{53} + 36 q^{54} - 40 q^{55} - 288 q^{56} - 40 q^{57} - 84 q^{58} - 20 q^{59} - 68 q^{60} - 52 q^{61} - 96 q^{63} - 112 q^{64} - 104 q^{65} - 20 q^{66} - 24 q^{67} + 8 q^{68} - 40 q^{69} - 12 q^{70} + 120 q^{71} - 52 q^{72} - 52 q^{73} - 96 q^{74} - 72 q^{75} - 40 q^{76} - 48 q^{77} + 64 q^{78} - 96 q^{80} + 268 q^{82} + 40 q^{83} - 28 q^{84} - 52 q^{86} - 52 q^{87} + 520 q^{88} - 52 q^{89} - 280 q^{90} - 336 q^{91} + 32 q^{92} + 8 q^{93} - 60 q^{94} - 104 q^{95} - 976 q^{96} - 192 q^{97} - 236 q^{98} - 120 q^{99} + O(q^{100}) \)

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.