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Properties

Label 1089.4.v
Level $1089$
Weight $4$
Character orbit 1089.v
Rep. character $\chi_{1089}(37,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $6560$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.v (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 16000 6640 9360
Cusp forms 15680 6560 9120
Eisenstein series 320 80 240

Trace form

\( 6560 q + 41 q^{2} + 601 q^{4} + 49 q^{5} - 33 q^{7} - 25 q^{8} + O(q^{10}) \) \( 6560 q + 41 q^{2} + 601 q^{4} + 49 q^{5} - 33 q^{7} - 25 q^{8} - 312 q^{10} + 165 q^{11} + 145 q^{13} - 6 q^{14} + 2561 q^{16} + 161 q^{17} - 144 q^{19} - 12 q^{20} + 1361 q^{22} + 694 q^{23} + 3559 q^{25} - 502 q^{26} + 106 q^{28} + 665 q^{29} + 69 q^{31} + 1784 q^{32} + 54 q^{34} + 521 q^{35} - 521 q^{37} + 512 q^{38} - 3925 q^{40} - 1447 q^{41} - 3042 q^{43} + 57 q^{44} - 1656 q^{46} - 9 q^{47} + 9355 q^{49} + 2147 q^{50} - 1344 q^{52} - 7557 q^{53} + 5331 q^{55} - 1067 q^{56} + 2777 q^{58} - 870 q^{59} + 1753 q^{61} + 5473 q^{62} + 12209 q^{64} + 5546 q^{65} - 1464 q^{67} + 4634 q^{68} - 2532 q^{70} + 4071 q^{71} - 3061 q^{73} - 1738 q^{74} - 2347 q^{76} + 2717 q^{77} + 221 q^{79} - 7473 q^{80} - 2905 q^{82} - 7888 q^{83} + 3205 q^{85} - 3625 q^{86} + 437 q^{88} - 6834 q^{89} + 1751 q^{91} + 5544 q^{92} - 1535 q^{94} + 10063 q^{95} - 1862 q^{97} + 8064 q^{98} + O(q^{100}) \)

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

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