Properties

Label 1064.2.ce
Level $1064$
Weight $2$
Character orbit 1064.ce
Rep. character $\chi_{1064}(115,\cdot)$
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.ce (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

\( 288 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 144 q^{9} + O(q^{10}) \) \( 288 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 144 q^{9} + 8 q^{11} + 30 q^{12} - 26 q^{14} - 2 q^{16} - 48 q^{22} - 36 q^{24} - 144 q^{25} - 20 q^{28} + 4 q^{30} + 8 q^{32} - 60 q^{36} - 60 q^{40} - 2 q^{42} - 16 q^{43} + 24 q^{44} + 16 q^{46} + 104 q^{50} - 40 q^{51} + 18 q^{52} + 114 q^{54} + 26 q^{56} - 24 q^{58} - 96 q^{59} + 68 q^{60} + 52 q^{64} - 40 q^{67} + 36 q^{68} - 10 q^{72} - 62 q^{74} - 52 q^{78} - 60 q^{80} - 128 q^{81} - 132 q^{82} + 64 q^{84} + 16 q^{86} - 6 q^{88} - 48 q^{89} + 80 q^{91} - 128 q^{92} + 90 q^{94} - 24 q^{96} - 22 q^{98} + 80 q^{99} + O(q^{100}) \)

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

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