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Properties

Label 165.6.m
Level $165$
Weight $6$
Character orbit 165.m
Rep. character $\chi_{165}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $160$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(165, [\chi])\).

Total New Old
Modular forms 496 160 336
Cusp forms 464 160 304
Eisenstein series 32 0 32

Trace form

\( 160 q - 8 q^{2} - 728 q^{4} + 392 q^{7} + 1096 q^{8} - 3240 q^{9} + O(q^{10}) \) \( 160 q - 8 q^{2} - 728 q^{4} + 392 q^{7} + 1096 q^{8} - 3240 q^{9} - 1600 q^{10} - 2612 q^{11} + 2564 q^{13} - 1884 q^{14} - 5104 q^{16} + 3616 q^{17} + 972 q^{18} - 3160 q^{19} - 3800 q^{20} - 20248 q^{22} - 8872 q^{23} - 324 q^{24} - 25000 q^{25} - 10248 q^{26} + 7132 q^{28} + 31432 q^{29} + 3600 q^{30} - 14404 q^{31} - 77816 q^{32} + 1116 q^{33} - 30592 q^{34} + 5800 q^{35} - 58968 q^{36} + 72052 q^{37} + 33516 q^{38} - 11160 q^{39} + 19200 q^{40} - 31868 q^{41} - 56952 q^{42} - 70760 q^{43} - 53656 q^{44} + 107620 q^{46} - 8608 q^{47} + 34848 q^{48} - 3092 q^{49} - 5000 q^{50} - 41508 q^{51} + 160428 q^{52} + 285104 q^{53} + 53700 q^{55} - 198744 q^{56} + 25992 q^{57} - 22380 q^{58} - 70240 q^{59} - 96692 q^{61} - 300136 q^{62} + 31752 q^{63} - 174212 q^{64} - 126600 q^{65} - 7164 q^{66} + 270968 q^{67} + 127360 q^{68} - 78048 q^{69} + 56300 q^{70} - 327528 q^{71} - 107244 q^{72} + 46676 q^{73} + 246060 q^{74} + 916288 q^{76} + 547772 q^{77} + 259776 q^{78} - 304512 q^{79} - 121600 q^{80} - 262440 q^{81} + 128556 q^{82} + 283324 q^{83} - 513648 q^{84} + 57800 q^{85} - 458512 q^{86} - 730872 q^{87} + 1638100 q^{88} - 692848 q^{89} + 32400 q^{90} - 825628 q^{91} - 185080 q^{92} - 73152 q^{93} - 385528 q^{94} + 459972 q^{96} - 238620 q^{97} - 467136 q^{98} + 421848 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)