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Properties

Label 1089.4.y
Level $1089$
Weight $4$
Character orbit 1089.y
Rep. character $\chi_{1089}(32,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $7880$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.y (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1089, [\chi])\).

Total New Old
Modular forms 7960 7960 0
Cusp forms 7880 7880 0
Eisenstein series 80 80 0

Trace form

\( 7880 q - 33 q^{2} - 38 q^{3} + 1559 q^{4} - 27 q^{5} - 110 q^{6} - 11 q^{7} + 54 q^{9} + O(q^{10}) \) \( 7880 q - 33 q^{2} - 38 q^{3} + 1559 q^{4} - 27 q^{5} - 110 q^{6} - 11 q^{7} + 54 q^{9} - 44 q^{10} + 33 q^{11} + 425 q^{12} - 11 q^{13} - 27 q^{14} - 441 q^{15} + 6215 q^{16} - 110 q^{18} - 44 q^{19} - 75 q^{20} + 275 q^{21} - 8 q^{22} + 225 q^{23} - 1452 q^{24} - 9659 q^{25} - 632 q^{27} - 44 q^{28} - 33 q^{29} - 616 q^{30} - 9 q^{31} - 33 q^{32} - 477 q^{33} - 173 q^{34} + 518 q^{36} - 36 q^{37} + 237 q^{38} + 275 q^{39} - 33 q^{41} - 2427 q^{42} - 11 q^{43} - 1191 q^{45} - 44 q^{46} - 27 q^{47} + 2181 q^{48} - 18727 q^{49} - 33 q^{50} - 5522 q^{51} - 11 q^{52} + 16214 q^{54} + 822 q^{55} - 1965 q^{56} + 2695 q^{57} - 545 q^{58} - 561 q^{59} + 2371 q^{60} - 11 q^{61} + 6941 q^{63} - 48964 q^{64} - 33 q^{65} + 1057 q^{66} + 765 q^{67} - 33 q^{68} + 3507 q^{69} - 107 q^{70} + 11242 q^{72} - 44 q^{73} - 33 q^{74} - 1519 q^{75} - 5951 q^{76} - 13434 q^{77} - 224 q^{78} - 11 q^{79} - 1738 q^{81} - 2156 q^{82} - 33 q^{83} - 616 q^{84} + 3949 q^{85} + 2409 q^{86} - 319 q^{87} - 2822 q^{88} - 14300 q^{90} - 3200 q^{91} + 27531 q^{92} - 2831 q^{93} - 22737 q^{95} - 319 q^{96} - 63 q^{97} - 8532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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