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Properties

Label 1045.6.cr
Level $1045$
Weight $6$
Character orbit 1045.cr
Rep. character $\chi_{1045}(3,\cdot)$
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.cr (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

\( 28608 q - 36 q^{2} - 36 q^{3} - 36 q^{5} - 72 q^{6} - 1080 q^{7} - 54 q^{8} + O(q^{10}) \) \( 28608 q - 36 q^{2} - 36 q^{3} - 36 q^{5} - 72 q^{6} - 1080 q^{7} - 54 q^{8} - 96 q^{10} - 48 q^{11} - 144 q^{12} - 36 q^{13} - 36 q^{15} - 72 q^{16} - 36 q^{17} - 61452 q^{20} - 192 q^{21} + 5424 q^{22} - 96 q^{23} - 23004 q^{25} + 10524 q^{26} - 54 q^{27} + 12252 q^{28} - 18 q^{30} - 108 q^{31} - 89124 q^{32} + 20130 q^{33} - 36 q^{35} - 72 q^{36} - 223644 q^{38} + 93504 q^{40} + 130068 q^{41} - 93348 q^{42} + 84480 q^{43} - 48 q^{45} - 108 q^{46} - 79764 q^{47} + 111708 q^{48} + 461898 q^{50} + 288648 q^{51} - 420 q^{52} - 143190 q^{53} + 561282 q^{55} + 548892 q^{57} - 459576 q^{58} + 228060 q^{60} - 72 q^{61} - 401580 q^{62} + 201648 q^{63} - 144 q^{65} + 382272 q^{66} + 688944 q^{67} + 220014 q^{68} - 207012 q^{70} - 72 q^{71} - 508644 q^{72} + 210528 q^{73} - 23952 q^{76} - 532008 q^{77} + 1813212 q^{78} - 394272 q^{80} - 469992 q^{81} - 489120 q^{82} - 726270 q^{83} + 1420572 q^{85} - 72 q^{86} + 620112 q^{87} - 83592 q^{88} + 922140 q^{90} + 28308 q^{91} + 2359668 q^{92} + 1311924 q^{93} + 519276 q^{95} - 6479184 q^{96} - 538068 q^{97} + 1191924 q^{98} + O(q^{100}) \)

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.