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Properties

Label 1064.2.cn
Level $1064$
Weight $2$
Character orbit 1064.cn
Rep. character $\chi_{1064}(837,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.cn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 328 288 40
Cusp forms 312 288 24
Eisenstein series 16 0 16

Trace form

\( 288 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 144 q^{9} + O(q^{10}) \) \( 288 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 144 q^{9} - 10 q^{12} + 26 q^{14} - 18 q^{16} - 16 q^{20} - 40 q^{22} - 8 q^{23} - 32 q^{24} + 144 q^{25} + 16 q^{26} - 44 q^{28} - 36 q^{30} + 32 q^{32} - 64 q^{34} + 20 q^{36} - 12 q^{40} - 18 q^{42} + 20 q^{44} + 4 q^{46} - 40 q^{47} - 32 q^{48} + 24 q^{50} + 70 q^{52} + 18 q^{54} - 64 q^{55} + 30 q^{56} + 8 q^{58} - 12 q^{60} + 72 q^{62} - 80 q^{63} + 52 q^{64} + 56 q^{66} - 32 q^{68} + 8 q^{70} - 80 q^{71} + 10 q^{72} - 18 q^{74} - 100 q^{78} + 40 q^{79} - 100 q^{80} - 160 q^{81} - 4 q^{82} - 112 q^{84} - 28 q^{86} + 48 q^{87} + 18 q^{88} + 16 q^{89} - 152 q^{90} + 64 q^{92} - 54 q^{94} - 8 q^{96} - 32 q^{97} - 58 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)