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Properties

Label 1045.6.cf
Level $1045$
Weight $6$
Character orbit 1045.cf
Rep. character $\chi_{1045}(7,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $9536$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.cf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 9664 9664 0
Cusp forms 9536 9536 0
Eisenstein series 128 128 0

Trace form

\( 9536 q - 10 q^{2} - 6 q^{3} - 50 q^{5} - 20 q^{6} - 1220 q^{7} - 40 q^{8} + O(q^{10}) \) \( 9536 q - 10 q^{2} - 6 q^{3} - 50 q^{5} - 20 q^{6} - 1220 q^{7} - 40 q^{8} - 24 q^{11} + 2136 q^{12} - 10 q^{13} - 6 q^{15} - 299020 q^{16} - 1920 q^{17} - 40 q^{18} + 49088 q^{20} + 2396 q^{22} - 5120 q^{23} - 12106 q^{25} + 10512 q^{26} + 1920 q^{27} - 10 q^{28} - 40 q^{30} - 48 q^{31} - 3866 q^{33} - 10 q^{35} - 1400060 q^{36} + 52424 q^{37} - 25572 q^{38} + 20470 q^{40} + 72280 q^{41} - 111214 q^{42} + 17192 q^{45} - 80 q^{46} - 54346 q^{47} - 27166 q^{48} + 28440 q^{50} - 20 q^{51} + 335350 q^{52} - 47724 q^{53} - 121470 q^{55} + 185216 q^{56} - 504220 q^{57} + 72592 q^{58} - 9094 q^{60} - 20 q^{61} + 158550 q^{62} - 243820 q^{63} - 53520 q^{66} + 86400 q^{67} - 245160 q^{68} + 59490 q^{70} - 12 q^{71} - 77770 q^{72} - 10 q^{73} - 711768 q^{75} + 923820 q^{77} - 476900 q^{78} - 321282 q^{80} - 7244180 q^{81} + 35854 q^{82} - 632240 q^{83} - 274770 q^{85} + 1298868 q^{86} - 476576 q^{88} + 668650 q^{90} - 9472 q^{91} - 121712 q^{92} - 352046 q^{93} - 336780 q^{95} + 2585520 q^{96} + 179338 q^{97} + O(q^{100}) \)

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.