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Properties

Label 2151.4.bc
Level $2151$
Weight $4$
Character orbit 2151.bc
Rep. character $\chi_{2151}(4,\cdot)$
Character field $\Q(\zeta_{357})$
Dimension $137856$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.bc (of order \(357\) and degree \(192\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2151 \)
Character field: \(\Q(\zeta_{357})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2151, [\chi])\).

Total New Old
Modular forms 138624 138624 0
Cusp forms 137856 137856 0
Eisenstein series 768 768 0

Trace form

\( 137856 q - 97 q^{2} - 194 q^{3} - 2961 q^{4} - 97 q^{5} - 194 q^{6} - 97 q^{7} - 386 q^{8} - 130 q^{9} + O(q^{10}) \) \( 137856 q - 97 q^{2} - 194 q^{3} - 2961 q^{4} - 97 q^{5} - 194 q^{6} - 97 q^{7} - 386 q^{8} - 130 q^{9} - 288 q^{10} - 157 q^{11} + 100 q^{12} - 97 q^{13} - 302 q^{14} - 8 q^{15} - 11505 q^{16} - 148 q^{17} + 62 q^{18} - 388 q^{19} + 279 q^{20} - 620 q^{21} - 58 q^{22} + 1462 q^{23} - 960 q^{24} - 17847 q^{25} - 1596 q^{26} - 620 q^{27} - 72 q^{28} - 1017 q^{29} - 365 q^{30} - 97 q^{31} + 1199 q^{32} + 612 q^{33} - 113 q^{34} + 3496 q^{35} - 8450 q^{36} - 388 q^{37} + 7780 q^{38} - 10942 q^{39} + 652 q^{40} - 753 q^{41} + 6234 q^{42} - 97 q^{43} - 4308 q^{44} + 6196 q^{45} - 468 q^{46} - 1545 q^{47} + 3210 q^{48} - 34691 q^{49} + 2804 q^{50} - 380 q^{51} + 1068 q^{52} + 2980 q^{53} - 21920 q^{54} + 112 q^{55} - 4015 q^{56} - 1958 q^{57} - 1550 q^{58} + 1537 q^{59} + 8675 q^{60} - 97 q^{61} - 318 q^{62} - 188 q^{63} + 91362 q^{64} - 261 q^{65} + 21823 q^{66} - 90 q^{67} + 5176 q^{68} - 3427 q^{69} + 5532 q^{70} - 12848 q^{71} - 15150 q^{72} - 360 q^{73} - 3561 q^{74} + 4056 q^{75} - 458 q^{76} - 949 q^{77} + 26078 q^{78} - 2437 q^{79} + 35588 q^{80} + 854 q^{81} - 3866 q^{82} - 8959 q^{83} - 4028 q^{84} + 373 q^{85} - 3765 q^{86} - 3290 q^{87} - 3729 q^{88} + 7924 q^{89} + 11977 q^{90} - 24 q^{91} + 8107 q^{92} + 17544 q^{93} + 2725 q^{94} - 47817 q^{95} - 5317 q^{96} - 97 q^{97} + 14112 q^{98} + 1904 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2151, [\chi])\) into newform subspaces

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