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Properties

Label 1064.2.b
Level $1064$
Weight $2$
Character orbit 1064.b
Rep. character $\chi_{1064}(533,\cdot)$
Character field $\Q$
Dimension $108$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 164 108 56
Cusp forms 156 108 48
Eisenstein series 8 0 8

Trace form

\( 108 q + 2 q^{2} - 2 q^{4} - 12 q^{6} + 4 q^{7} + 14 q^{8} - 108 q^{9} + O(q^{10}) \) \( 108 q + 2 q^{2} - 2 q^{4} - 12 q^{6} + 4 q^{7} + 14 q^{8} - 108 q^{9} + 16 q^{10} - 28 q^{12} - 2 q^{14} + 6 q^{16} + 8 q^{17} + 2 q^{18} - 8 q^{22} + 16 q^{23} - 16 q^{24} - 116 q^{25} - 4 q^{26} + 10 q^{28} - 20 q^{30} + 22 q^{32} - 6 q^{36} - 16 q^{39} + 16 q^{40} - 8 q^{41} + 20 q^{42} + 28 q^{44} + 24 q^{46} - 40 q^{48} + 108 q^{49} - 46 q^{50} + 20 q^{52} + 104 q^{54} - 64 q^{55} - 14 q^{56} - 44 q^{58} + 92 q^{60} + 36 q^{62} - 20 q^{63} - 38 q^{64} - 32 q^{65} - 8 q^{66} - 12 q^{68} + 8 q^{71} - 34 q^{72} + 40 q^{73} - 12 q^{78} + 40 q^{79} - 76 q^{80} + 108 q^{81} - 8 q^{82} - 60 q^{86} + 48 q^{87} - 72 q^{88} + 40 q^{89} - 100 q^{90} - 92 q^{92} + 100 q^{94} - 32 q^{95} + 124 q^{96} + 8 q^{97} + 2 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \)