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Properties

Label 1089.4.n
Level $1089$
Weight $4$
Character orbit 1089.n
Rep. character $\chi_{1089}(124,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2528$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.n (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 3264 2656 608
Cusp forms 3072 2528 544
Eisenstein series 192 128 64

Trace form

\( 2528 q - q^{2} + 4 q^{3} + 1235 q^{4} - 5 q^{5} - 8 q^{6} + 3 q^{7} + 140 q^{8} - 88 q^{9} + O(q^{10}) \) \( 2528 q - q^{2} + 4 q^{3} + 1235 q^{4} - 5 q^{5} - 8 q^{6} + 3 q^{7} + 140 q^{8} - 88 q^{9} + 64 q^{10} + 214 q^{12} + 3 q^{13} + 35 q^{14} - 128 q^{15} + 4659 q^{16} + 512 q^{17} + 186 q^{18} + 282 q^{19} + 155 q^{20} + 142 q^{21} - 876 q^{23} - 726 q^{24} + 7247 q^{25} - 900 q^{26} - 548 q^{27} + 300 q^{28} - 109 q^{29} + 1062 q^{30} + 39 q^{31} + 1704 q^{32} - 228 q^{34} + 2412 q^{35} + 122 q^{36} + 156 q^{37} + 319 q^{38} - 526 q^{39} - 23 q^{40} - 1303 q^{41} + 1731 q^{42} - 334 q^{43} + 1594 q^{45} - 36 q^{46} - 365 q^{47} - 1054 q^{48} + 13135 q^{49} - 66 q^{50} + 99 q^{51} + 243 q^{52} - 3972 q^{53} - 3034 q^{54} - 3162 q^{56} + 2658 q^{57} + 791 q^{58} - 312 q^{59} + 1993 q^{60} + 3 q^{61} + 5126 q^{62} + 1354 q^{63} - 33060 q^{64} + 3080 q^{65} + 1642 q^{67} - 5170 q^{68} + 4257 q^{69} + 1524 q^{70} + 2788 q^{71} + 2113 q^{72} - 2472 q^{73} - 1473 q^{74} + 867 q^{75} + 992 q^{76} - 15016 q^{78} + 1191 q^{79} - 76 q^{80} + 2540 q^{81} - 3088 q^{82} - 1217 q^{83} + 597 q^{84} + 473 q^{85} + 1713 q^{86} + 1650 q^{87} - 5928 q^{89} + 7876 q^{90} + 2896 q^{91} + 1873 q^{92} - 12030 q^{93} - 1621 q^{94} - 5799 q^{95} - 13715 q^{96} - 1068 q^{97} - 12848 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)