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Properties

Label 1089.6.bc
Level $1089$
Weight $6$
Character orbit 1089.bc
Rep. character $\chi_{1089}(4,\cdot)$
Character field $\Q(\zeta_{165})$
Dimension $52640$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1089.bc (of order \(165\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{165})\)
Sturm bound: \(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1089, [\chi])\).

Total New Old
Modular forms 52960 52960 0
Cusp forms 52640 52640 0
Eisenstein series 320 320 0

Trace form

\( 52640 q - 33 q^{2} - 82 q^{3} - 10537 q^{4} - 41 q^{5} - 382 q^{6} - 41 q^{7} - 804 q^{8} + 534 q^{9} + O(q^{10}) \) \( 52640 q - 33 q^{2} - 82 q^{3} - 10537 q^{4} - 41 q^{5} - 382 q^{6} - 41 q^{7} - 804 q^{8} + 534 q^{9} - 16 q^{10} - 79 q^{11} - 11699 q^{12} - 41 q^{13} + 87 q^{14} + 5431 q^{15} - 167017 q^{16} - 7800 q^{17} + 6406 q^{18} - 2846 q^{19} + 4151 q^{20} + 4011 q^{21} + 972 q^{22} + 30 q^{23} - 30692 q^{24} - 406291 q^{25} + 21788 q^{26} - 12325 q^{27} + 4060 q^{28} + 14142 q^{29} + 26228 q^{30} - 41 q^{31} - 59300 q^{32} - 46679 q^{33} + 7556 q^{34} - 37694 q^{35} + 46822 q^{36} - 164 q^{37} - 126209 q^{38} + 33070 q^{39} - 3080 q^{40} + 78147 q^{41} - 71700 q^{42} + 6270 q^{43} - 21826 q^{44} + 12305 q^{45} - 356 q^{46} - 31853 q^{47} - 120091 q^{48} - 1551087 q^{49} + 70126 q^{50} + 606947 q^{51} + 3991 q^{52} + 67508 q^{53} + 854054 q^{54} - 22482 q^{55} - 77358 q^{56} + 493947 q^{57} - 14961 q^{58} - 53226 q^{59} + 80904 q^{60} - 41 q^{61} + 84534 q^{62} - 43797 q^{63} + 5279388 q^{64} - 264408 q^{65} - 317958 q^{66} - 21090 q^{67} + 276810 q^{68} - 333352 q^{69} + 9488 q^{70} - 92916 q^{71} + 619721 q^{72} + 160720 q^{73} + 628315 q^{74} + 190332 q^{75} + 191148 q^{76} - 415909 q^{77} + 133746 q^{78} - 161609 q^{79} - 3234788 q^{80} + 212394 q^{81} - 167148 q^{82} + 7142 q^{83} + 163391 q^{84} + 73359 q^{85} - 550585 q^{86} - 637561 q^{87} - 844920 q^{88} - 383890 q^{89} - 666526 q^{90} + 519824 q^{91} - 266135 q^{92} - 555723 q^{93} + 57962 q^{94} + 775133 q^{95} + 2239356 q^{96} - 261698 q^{97} + 2298720 q^{98} - 787946 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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