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Properties

Label 1064.2.cp
Level $1064$
Weight $2$
Character orbit 1064.cp
Rep. character $\chi_{1064}(715,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
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.cp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 328 240 88
Cusp forms 312 240 72
Eisenstein series 16 0 16

Trace form

\( 240 q - 4 q^{4} + 4 q^{6} + 120 q^{9} + O(q^{10}) \) \( 240 q - 4 q^{4} + 4 q^{6} + 120 q^{9} - 12 q^{10} + 4 q^{16} - 16 q^{19} + 68 q^{20} + 10 q^{24} + 120 q^{25} + 12 q^{26} - 88 q^{30} - 30 q^{32} + 18 q^{34} + 32 q^{36} - 24 q^{38} + 12 q^{40} - 24 q^{41} + 22 q^{44} + 90 q^{48} - 240 q^{49} + 48 q^{51} - 78 q^{52} - 32 q^{54} - 8 q^{57} - 44 q^{58} + 30 q^{60} - 12 q^{62} - 64 q^{64} + 4 q^{68} + 36 q^{70} + 42 q^{72} - 8 q^{74} - 58 q^{76} - 24 q^{78} + 6 q^{80} - 112 q^{81} - 48 q^{82} - 80 q^{83} + 60 q^{86} - 48 q^{90} - 56 q^{92} - 120 q^{96} + 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)