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Properties

Label 1064.2.dj
Level $1064$
Weight $2$
Character orbit 1064.dj
Rep. character $\chi_{1064}(117,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $936$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.dj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1064 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1064, [\chi])\).

Total New Old
Modular forms 984 984 0
Cusp forms 936 936 0
Eisenstein series 48 48 0

Trace form

\( 936 q - 3 q^{2} - 3 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} + O(q^{10}) \) \( 936 q - 3 q^{2} - 3 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 9 q^{10} - 18 q^{12} - 27 q^{14} - 24 q^{15} - 3 q^{16} - 18 q^{17} - 6 q^{22} - 6 q^{23} + 18 q^{24} - 6 q^{25} + 15 q^{28} + 3 q^{30} - 18 q^{31} - 18 q^{32} - 18 q^{33} - 63 q^{36} - 36 q^{38} - 12 q^{39} - 9 q^{40} - 87 q^{42} + 78 q^{44} - 126 q^{47} - 99 q^{48} - 6 q^{49} + 9 q^{50} - 9 q^{52} - 9 q^{54} + 90 q^{55} - 24 q^{57} - 42 q^{58} + 48 q^{60} + 81 q^{62} - 96 q^{63} - 6 q^{64} - 18 q^{65} + 45 q^{66} - 9 q^{68} - 63 q^{70} - 24 q^{71} - 54 q^{72} + 54 q^{73} + 51 q^{74} - 75 q^{78} - 6 q^{79} - 9 q^{80} + 12 q^{81} - 9 q^{82} - 9 q^{84} + 30 q^{86} - 9 q^{88} - 18 q^{89} - 306 q^{90} - 54 q^{92} - 6 q^{95} + 135 q^{96} - 102 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1064, [\chi])\) into newform subspaces

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