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Properties

Label 1521.4.bi
Level $1521$
Weight $4$
Character orbit 1521.bi
Rep. character $\chi_{1521}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $13056$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.bi (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1521, [\chi])\).

Total New Old
Modular forms 13152 13152 0
Cusp forms 13056 13056 0
Eisenstein series 96 96 0

Trace form

\( 13056 q - 11 q^{2} - 25 q^{3} - 4347 q^{4} - 11 q^{5} - 8 q^{6} - 2 q^{7} - 22 q^{8} - 41 q^{9} + O(q^{10}) \) \( 13056 q - 11 q^{2} - 25 q^{3} - 4347 q^{4} - 11 q^{5} - 8 q^{6} - 2 q^{7} - 22 q^{8} - 41 q^{9} - 58 q^{10} + 5 q^{11} - 65 q^{12} + 132 q^{13} + 117 q^{14} - 543 q^{15} - 17211 q^{16} + 86 q^{17} + 945 q^{18} + 6 q^{19} + 130 q^{20} - 19 q^{21} + 40 q^{22} - 3352 q^{23} - 1046 q^{24} + 13389 q^{25} - 466 q^{26} + 68 q^{27} + 262 q^{28} - 1243 q^{29} - 650 q^{30} - 71 q^{31} - 83 q^{32} + 779 q^{33} - 19 q^{34} + 515 q^{35} + 342 q^{36} + 34 q^{37} + 657 q^{38} - 5755 q^{39} + 191 q^{40} + 114 q^{41} - 1123 q^{42} + 70 q^{43} - 932 q^{44} - 3088 q^{45} - 138 q^{46} + 4959 q^{47} + 4986 q^{48} + 25814 q^{49} - 1565 q^{50} - 2248 q^{51} - 399 q^{52} - 1148 q^{53} - 959 q^{54} - 175 q^{55} + 1131 q^{56} + 2899 q^{57} + 1241 q^{58} - 2403 q^{59} + 1057 q^{60} - 434 q^{61} + 601 q^{62} - 10375 q^{63} - 68010 q^{64} + 1156 q^{65} - 19686 q^{66} - 308 q^{67} + 2867 q^{68} + 1486 q^{69} - 875 q^{70} - 354 q^{71} + 15590 q^{72} + 292 q^{73} + 1972 q^{74} + 3880 q^{75} - 222 q^{76} + 2399 q^{77} + 3458 q^{78} + 667 q^{79} + 4664 q^{80} + 3767 q^{81} - 1321 q^{82} + 4705 q^{83} - 10350 q^{84} + 1175 q^{85} + 2051 q^{86} + 1103 q^{87} - 1787 q^{88} + 8566 q^{89} - 5205 q^{90} - 827 q^{91} + 3049 q^{92} - 10431 q^{93} + 1352 q^{94} - 10090 q^{95} + 4470 q^{96} + 1042 q^{97} + 1521 q^{98} + 5555 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.