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Properties

Label 1045.6.y
Level $1045$
Weight $6$
Character orbit 1045.y
Rep. character $\chi_{1045}(151,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1600$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2416 1600 816
Cusp forms 2384 1600 784
Eisenstein series 32 0 32

Trace form

\( 1600 q - 6400 q^{4} + 80 q^{6} + 32664 q^{9} + O(q^{10}) \) \( 1600 q - 6400 q^{4} + 80 q^{6} + 32664 q^{9} + 936 q^{11} - 102400 q^{16} + 10840 q^{17} + 4470 q^{19} + 8608 q^{23} - 3840 q^{24} - 250000 q^{25} + 112 q^{26} + 417776 q^{36} + 29130 q^{38} - 108660 q^{39} - 270404 q^{42} - 198616 q^{44} + 78752 q^{47} + 824900 q^{49} - 244470 q^{57} + 165184 q^{58} + 41960 q^{61} + 232160 q^{62} - 1919560 q^{64} - 183728 q^{66} - 520320 q^{68} - 183640 q^{73} + 348100 q^{74} - 738916 q^{77} + 72600 q^{80} - 2223076 q^{81} - 365576 q^{82} - 534440 q^{83} - 223736 q^{92} - 26352 q^{93} - 2156600 q^{96} + 406688 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)