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Properties

Label 1045.6.i
Level $1045$
Weight $6$
Character orbit 1045.i
Rep. character $\chi_{1045}(771,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $672$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1208 672 536
Cusp forms 1192 672 520
Eisenstein series 16 0 16

Trace form

\( 672 q + 72 q^{3} - 5524 q^{4} + 180 q^{6} + 376 q^{7} - 27864 q^{9} + O(q^{10}) \) \( 672 q + 72 q^{3} - 5524 q^{4} + 180 q^{6} + 376 q^{7} - 27864 q^{9} + 100 q^{10} - 6912 q^{12} - 300 q^{13} + 1800 q^{15} - 94020 q^{16} - 956 q^{17} - 11756 q^{19} + 4608 q^{21} + 1936 q^{22} + 4436 q^{23} + 16200 q^{24} - 210000 q^{25} + 21432 q^{26} - 46656 q^{27} - 11640 q^{28} - 8168 q^{29} - 16 q^{31} + 15020 q^{32} + 8712 q^{33} + 4648 q^{34} - 517556 q^{36} + 32624 q^{37} + 101700 q^{38} - 32048 q^{39} - 21600 q^{40} + 10728 q^{41} + 27124 q^{42} + 44832 q^{43} - 11600 q^{45} + 162184 q^{46} - 29296 q^{47} + 34984 q^{48} + 1814312 q^{49} + 87888 q^{51} - 8064 q^{52} - 8264 q^{53} - 77040 q^{54} - 92216 q^{56} - 52400 q^{57} + 33000 q^{58} + 25844 q^{59} + 2700 q^{60} - 50576 q^{61} + 54132 q^{62} - 123604 q^{63} + 3500432 q^{64} + 99220 q^{66} + 19696 q^{67} + 396328 q^{68} - 280784 q^{69} + 39200 q^{70} + 120636 q^{71} - 278264 q^{72} + 307888 q^{73} - 510992 q^{74} - 90000 q^{75} + 236608 q^{76} + 467156 q^{78} + 21844 q^{79} - 16400 q^{80} - 2134568 q^{81} - 297284 q^{82} + 165536 q^{83} - 15848 q^{84} + 132400 q^{85} + 31120 q^{86} + 177808 q^{87} - 185856 q^{88} + 217920 q^{89} - 38700 q^{90} - 457008 q^{91} + 292584 q^{92} - 645384 q^{93} - 931192 q^{94} - 91400 q^{95} - 3591488 q^{96} - 18908 q^{97} + 981608 q^{98} + O(q^{100}) \)

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.

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

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)