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Properties

Label 1089.4.f
Level $1089$
Weight $4$
Character orbit 1089.f
Rep. character $\chi_{1089}(487,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $524$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1680 556 1124
Cusp forms 1488 524 964
Eisenstein series 192 32 160

Trace form

\( 524 q - 3 q^{2} - 515 q^{4} + 13 q^{5} + 11 q^{7} - 69 q^{8} + O(q^{10}) \) \( 524 q - 3 q^{2} - 515 q^{4} + 13 q^{5} + 11 q^{7} - 69 q^{8} - 136 q^{10} - 31 q^{13} + 274 q^{14} - 1819 q^{16} + 117 q^{17} - 100 q^{19} + 32 q^{20} - 980 q^{23} - 3128 q^{25} - 770 q^{26} + 150 q^{28} + 621 q^{29} - 531 q^{31} + 1740 q^{32} + 2522 q^{34} + 477 q^{35} + 207 q^{37} - 348 q^{38} - 1252 q^{40} - 1491 q^{41} - 2998 q^{43} - 1612 q^{46} + 695 q^{47} - 5418 q^{49} - 1725 q^{50} + 878 q^{52} - 591 q^{53} - 2244 q^{56} - 2152 q^{58} + 146 q^{59} + 1797 q^{61} + 2184 q^{62} - 3555 q^{64} + 6030 q^{65} + 6058 q^{67} + 4590 q^{68} + 528 q^{70} + 1743 q^{71} - 905 q^{73} - 1782 q^{74} - 9046 q^{76} - 747 q^{79} - 5974 q^{80} + 15 q^{82} - 7932 q^{83} + 7385 q^{85} - 5553 q^{86} - 738 q^{89} + 6713 q^{91} + 7396 q^{92} + 11874 q^{94} + 2451 q^{95} + 1578 q^{97} + 16380 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)