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Properties

Label 1089.4.u
Level $1089$
Weight $4$
Character orbit 1089.u
Rep. character $\chi_{1089}(34,\cdot)$
Character field $\Q(\zeta_{33})$
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.u (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{33})\)
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

\( 7880 q - 5 q^{2} - 42 q^{3} + 1559 q^{4} - 9 q^{5} + 34 q^{6} - 9 q^{7} - 164 q^{8} - 74 q^{9} + O(q^{10}) \) \( 7880 q - 5 q^{2} - 42 q^{3} + 1559 q^{4} - 9 q^{5} + 34 q^{6} - 9 q^{7} - 164 q^{8} - 74 q^{9} - 68 q^{10} + 11 q^{11} - 7 q^{12} - 9 q^{13} - 41 q^{14} + 405 q^{15} + 6215 q^{16} - 536 q^{17} + 350 q^{18} + 144 q^{19} - 249 q^{20} + 153 q^{21} - 44 q^{22} - 93 q^{23} - 2544 q^{24} + 9641 q^{25} + 316 q^{26} - 48 q^{27} - 324 q^{28} - 197 q^{29} - 618 q^{30} - 9 q^{31} + 535 q^{32} - 99 q^{33} + 187 q^{34} - 1136 q^{35} + 1126 q^{36} - 36 q^{37} + 327 q^{38} - 1179 q^{39} + 326 q^{40} + 97 q^{41} - 1001 q^{42} + 333 q^{43} + 1298 q^{44} + 1987 q^{45} - 68 q^{46} - 417 q^{47} - 291 q^{48} + 18709 q^{49} + 685 q^{50} + 6432 q^{51} - 249 q^{52} + 7636 q^{53} + 14084 q^{54} - 902 q^{55} - 879 q^{56} + 3937 q^{57} + 463 q^{58} - 831 q^{59} + 2805 q^{60} - 9 q^{61} + 2800 q^{62} + 6367 q^{63} - 48964 q^{64} + 2119 q^{65} + 3905 q^{66} + 765 q^{67} + 1249 q^{68} - 3047 q^{69} + 265 q^{70} - 1252 q^{71} - 8304 q^{72} + 2448 q^{73} + 487 q^{74} + 4109 q^{75} + 4947 q^{76} + 4620 q^{77} - 2412 q^{78} - 1197 q^{79} - 1732 q^{80} - 1034 q^{81} - 2156 q^{82} + 931 q^{83} + 6922 q^{84} + 3481 q^{85} + 1031 q^{86} + 2045 q^{87} + 3586 q^{88} + 19444 q^{89} - 25276 q^{90} - 5944 q^{91} + 2645 q^{92} + 3505 q^{93} + 1604 q^{94} + 9921 q^{95} - 845 q^{96} + 45 q^{97} + 3300 q^{98} + 7810 q^{99} + O(q^{100}) \)

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.