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Properties

Label 387.4.m
Level $387$
Weight $4$
Character orbit 387.m
Rep. character $\chi_{387}(50,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $260$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 387.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(387, [\chi])\).

Total New Old
Modular forms 268 268 0
Cusp forms 260 260 0
Eisenstein series 8 8 0

Trace form

\( 260 q - 3 q^{3} - 514 q^{4} - 6 q^{5} + 51 q^{6} - 3 q^{9} + O(q^{10}) \) \( 260 q - 3 q^{3} - 514 q^{4} - 6 q^{5} + 51 q^{6} - 3 q^{9} + 6 q^{10} + 69 q^{11} + 78 q^{12} + 13 q^{13} - 267 q^{14} - 109 q^{15} - 2002 q^{16} + 171 q^{17} + 378 q^{18} + 39 q^{19} + 21 q^{20} + 211 q^{21} - 54 q^{22} - 248 q^{24} + 6098 q^{25} + 24 q^{26} - 414 q^{27} + 210 q^{28} + 246 q^{29} + 723 q^{30} + 118 q^{31} - 690 q^{32} + 1209 q^{33} + 71 q^{36} - 6 q^{37} + 411 q^{38} - 375 q^{39} - 348 q^{40} - 1497 q^{41} + 963 q^{42} - 427 q^{43} - 195 q^{45} + 18 q^{46} + 564 q^{47} - 1992 q^{48} - 12838 q^{49} - 1602 q^{50} - 1317 q^{51} - 146 q^{52} - 1333 q^{54} - 381 q^{55} + 189 q^{57} - 15 q^{58} + 261 q^{59} + 1825 q^{60} - 24 q^{62} + 567 q^{63} + 15128 q^{64} + 2292 q^{66} - 404 q^{67} + 3195 q^{68} + 2781 q^{69} + 279 q^{70} - 840 q^{71} - 7353 q^{72} - 1869 q^{73} + 7740 q^{74} + 234 q^{75} - 3 q^{77} - 1346 q^{78} - 422 q^{79} - 207 q^{80} - 643 q^{81} - 891 q^{83} + 2789 q^{84} - 375 q^{85} - 4143 q^{86} - 1875 q^{87} + 3780 q^{88} + 3066 q^{89} + 829 q^{90} + 1344 q^{91} + 21 q^{92} - 1059 q^{93} - 1836 q^{94} - 2607 q^{95} + 406 q^{96} - 293 q^{97} - 7899 q^{98} - 2327 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

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