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Properties

Label 1089.4.m
Level $1089$
Weight $4$
Character orbit 1089.m
Rep. character $\chi_{1089}(100,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $1640$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 4000 1660 2340
Cusp forms 3920 1640 2280
Eisenstein series 80 20 60

Trace form

\( 1640 q + 9 q^{2} - 651 q^{4} + q^{5} - 7 q^{7} + 35 q^{8} + O(q^{10}) \) \( 1640 q + 9 q^{2} - 651 q^{4} + q^{5} - 7 q^{7} + 35 q^{8} + 167 q^{10} - 165 q^{11} - 215 q^{13} + 251 q^{14} - 2591 q^{16} + 39 q^{17} - 131 q^{19} - 453 q^{20} - 781 q^{22} - 649 q^{23} - 3669 q^{25} + 327 q^{26} + 309 q^{28} + 35 q^{29} - 509 q^{31} + 271 q^{32} - 99 q^{34} + 759 q^{35} + 571 q^{37} - 727 q^{38} + 2390 q^{40} - 213 q^{41} + 577 q^{43} - 1892 q^{44} - 9 q^{46} - 531 q^{47} - 9915 q^{49} - 3437 q^{50} + 1599 q^{52} + 5947 q^{53} - 3421 q^{55} + 1112 q^{56} - 2472 q^{58} + 1215 q^{59} + 157 q^{61} - 68 q^{62} - 8279 q^{64} - 1221 q^{65} + 1419 q^{67} + 1651 q^{68} + 4017 q^{70} - 1691 q^{71} - 1459 q^{73} + 2273 q^{74} - 5098 q^{76} - 5797 q^{77} - 3811 q^{79} - 5742 q^{80} + 3255 q^{82} + 743 q^{83} + 1945 q^{85} - 1375 q^{86} - 2167 q^{88} + 6879 q^{89} + 5779 q^{91} + 3071 q^{92} + 10290 q^{94} - 4773 q^{95} + 2877 q^{97} - 1079 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)