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Properties

Label 387.4.ba
Level $387$
Weight $4$
Character orbit 387.ba
Rep. character $\chi_{387}(4,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1560$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 387.ba (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(176\)

Dimensions

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

Total New Old
Modular forms 1608 1608 0
Cusp forms 1560 1560 0
Eisenstein series 48 48 0

Trace form

\( 1560 q - q^{2} - 12 q^{3} + 507 q^{4} + 15 q^{5} - 76 q^{6} - 148 q^{8} + 90 q^{9} + O(q^{10}) \) \( 1560 q - q^{2} - 12 q^{3} + 507 q^{4} + 15 q^{5} - 76 q^{6} - 148 q^{8} + 90 q^{9} - 52 q^{10} + 45 q^{11} + 24 q^{12} - 29 q^{13} - 145 q^{14} - 64 q^{15} + 1995 q^{16} - 248 q^{17} - 318 q^{18} - 350 q^{19} - 159 q^{20} + 157 q^{21} + 53 q^{22} - 5 q^{23} + 1084 q^{24} + 3045 q^{25} - 676 q^{26} + 558 q^{27} + 204 q^{28} + 427 q^{29} - 1313 q^{30} - 305 q^{31} + 1689 q^{32} + 653 q^{33} - 439 q^{34} + 1726 q^{35} + 1004 q^{36} + 288 q^{37} - 921 q^{38} - 40 q^{39} + 341 q^{40} + 81 q^{41} + 2514 q^{42} + 81 q^{43} - 1536 q^{44} - 1400 q^{45} + 956 q^{46} - 385 q^{47} - 2392 q^{48} - 35340 q^{49} - 6300 q^{50} + 2850 q^{51} + 715 q^{52} + 1100 q^{53} + 312 q^{54} - 520 q^{55} - 1562 q^{56} + 1804 q^{57} - 37 q^{58} + 571 q^{59} - 1786 q^{60} + 871 q^{61} - 4004 q^{62} + 1119 q^{63} - 15156 q^{64} + 1163 q^{65} - 1504 q^{66} + 1357 q^{67} + 4314 q^{68} - 7016 q^{69} - 1844 q^{70} - 2876 q^{71} + 569 q^{72} + 1792 q^{73} - 555 q^{74} - 4999 q^{75} - 1949 q^{76} + 4577 q^{77} + 5092 q^{78} - 432 q^{79} + 32604 q^{80} - 12138 q^{81} - 2140 q^{82} + 1813 q^{83} - 10075 q^{84} + 238 q^{85} + 1966 q^{86} + 5514 q^{87} + 3891 q^{88} + 12716 q^{89} - 18062 q^{90} + 6890 q^{91} + 364 q^{92} - 8050 q^{93} + 2843 q^{94} - 681 q^{95} + 4150 q^{96} - 479 q^{97} + 7518 q^{98} + 12461 q^{99} + O(q^{100}) \)

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.