Properties

Label 1045.6.cs
Level $1045$
Weight $6$
Character orbit 1045.cs
Rep. character $\chi_{1045}(17,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $28608$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.cs (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 28992 28992 0
Cusp forms 28608 28608 0
Eisenstein series 384 384 0

Trace form

\( 28608 q - 60 q^{2} - 36 q^{3} - 36 q^{5} - 120 q^{6} + 1740 q^{7} - 30 q^{8} + O(q^{10}) \) \( 28608 q - 60 q^{2} - 36 q^{3} - 36 q^{5} - 120 q^{6} + 1740 q^{7} - 30 q^{8} - 48 q^{11} - 48 q^{12} - 60 q^{13} - 36 q^{15} - 72 q^{16} - 60 q^{17} - 120 q^{18} - 61452 q^{20} - 5520 q^{22} - 96 q^{23} + 22932 q^{25} - 36 q^{26} - 18 q^{27} - 60 q^{28} - 30 q^{30} - 36 q^{31} - 14286 q^{33} - 60 q^{35} - 72 q^{36} - 72 q^{37} - 223644 q^{38} - 60 q^{40} - 217020 q^{41} + 93276 q^{42} - 48 q^{45} - 60 q^{46} + 79692 q^{47} + 74844 q^{48} - 30 q^{50} - 120 q^{51} - 60 q^{52} + 143118 q^{53} - 537342 q^{55} - 384 q^{56} + 863700 q^{57} - 459576 q^{58} - 228132 q^{60} - 120 q^{61} - 475740 q^{62} - 60 q^{63} + 568896 q^{66} + 688944 q^{67} + 366690 q^{68} + 206940 q^{70} - 72 q^{71} + 233220 q^{72} - 60 q^{73} - 72 q^{75} + 1076400 q^{77} + 1814748 q^{78} + 345048 q^{80} - 469992 q^{81} + 1039968 q^{82} - 30 q^{83} - 1648620 q^{85} - 72 q^{86} + 365352 q^{88} + 1536900 q^{90} + 28308 q^{91} - 2358972 q^{92} - 1311996 q^{93} - 60 q^{95} + 7756560 q^{96} - 538068 q^{97} + O(q^{100}) \)

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

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