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Properties

Label 1045.6.bp
Level $1045$
Weight $6$
Character orbit 1045.bp
Rep. character $\chi_{1045}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4768$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1045, [\chi])\).

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q - 56 q^{5} - 24 q^{6} + 342 q^{7} + O(q^{10}) \) \( 4768 q - 56 q^{5} - 24 q^{6} + 342 q^{7} + 8 q^{11} + 298984 q^{16} - 1158 q^{17} + 12256 q^{20} + 5072 q^{23} + 19744 q^{25} + 1736 q^{26} - 23052 q^{28} - 8420 q^{30} - 12656 q^{35} - 1585960 q^{36} - 86250 q^{38} - 17140 q^{42} - 21996 q^{43} - 32776 q^{45} + 80904 q^{47} + 200980 q^{55} - 139026 q^{57} - 80052 q^{58} - 24 q^{61} + 151164 q^{62} - 274922 q^{63} - 373664 q^{66} + 221532 q^{68} - 270968 q^{73} - 304 q^{76} + 1030462 q^{77} + 94276 q^{80} + 7714064 q^{81} - 438756 q^{82} - 446812 q^{83} - 170980 q^{85} + 415352 q^{87} + 434760 q^{92} + 746836 q^{93} + 256414 q^{95} - 971832 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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