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Properties

Label 1849.4.m
Level $1849$
Weight $4$
Character orbit 1849.m
Rep. character $\chi_{1849}(4,\cdot)$
Character field $\Q(\zeta_{301})$
Dimension $118944$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.m (of order \(301\) and degree \(252\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1849 \)
Character field: \(\Q(\zeta_{301})\)
Sturm bound: \(630\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1849, [\chi])\).

Total New Old
Modular forms 119448 119448 0
Cusp forms 118944 118944 0
Eisenstein series 504 504 0

Trace form

\( 118944 q - 249 q^{2} - 255 q^{3} + 1621 q^{4} - 235 q^{5} - 274 q^{6} - 354 q^{7} - 319 q^{8} + 4077 q^{9} + O(q^{10}) \) \( 118944 q - 249 q^{2} - 255 q^{3} + 1621 q^{4} - 235 q^{5} - 274 q^{6} - 354 q^{7} - 319 q^{8} + 4077 q^{9} - 197 q^{10} - 351 q^{11} - 291 q^{12} - 369 q^{13} + 1546 q^{14} - 367 q^{15} + 7093 q^{16} - 431 q^{17} + 156 q^{18} - 3767 q^{19} + 105 q^{20} - 170 q^{21} - 679 q^{22} + 3063 q^{23} + 679 q^{24} + 11079 q^{25} - 397 q^{26} - 231 q^{27} - 287 q^{28} + 109 q^{29} + 4217 q^{30} - 2469 q^{31} - 693 q^{32} + 2336 q^{33} + 325 q^{34} - 4688 q^{35} - 101602 q^{36} - 1278 q^{37} - 1165 q^{38} + 1313 q^{39} - 1521 q^{40} - 471 q^{41} + 1572 q^{42} - 1919 q^{43} - 5810 q^{44} - 1277 q^{45} + 2528 q^{46} - 95 q^{47} - 163 q^{48} - 136858 q^{49} + 24 q^{50} - 1782 q^{51} + 1189 q^{52} + 2309 q^{53} + 2489 q^{54} + 1477 q^{55} + 321 q^{56} - 152 q^{57} - 593 q^{58} - 809 q^{59} - 647 q^{60} + 81 q^{61} - 1181 q^{62} + 444 q^{63} + 34473 q^{64} - 2721 q^{65} - 55618 q^{66} + 141 q^{67} + 4233 q^{68} - 2969 q^{69} + 7440 q^{70} + 2173 q^{71} - 36854 q^{72} + 1899 q^{73} + 1134 q^{74} + 27 q^{75} + 6766 q^{76} + 3704 q^{77} + 2645 q^{78} - 2910 q^{79} - 11876 q^{80} + 25104 q^{81} - 46077 q^{82} + 2612 q^{83} - 3074 q^{84} + 3188 q^{85} - 10313 q^{86} - 20998 q^{87} - 10215 q^{88} + 5553 q^{89} - 49696 q^{90} + 502 q^{91} - 4874 q^{92} - 4252 q^{93} - 29535 q^{94} + 4148 q^{95} + 2808 q^{96} + 37709 q^{97} + 8783 q^{98} + 16354 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1849, [\chi])\) into newform subspaces

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