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Properties

Label 1849.4.i
Level $1849$
Weight $4$
Character orbit 1849.i
Rep. character $\chi_{1849}(44,\cdot)$
Character field $\Q(\zeta_{43})$
Dimension $19824$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.i (of order \(43\) and degree \(42\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1849 \)
Character field: \(\Q(\zeta_{43})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 19908 19908 0
Cusp forms 19824 19824 0
Eisenstein series 84 84 0

Trace form

\( 19824 q - 45 q^{2} - 39 q^{3} - 1915 q^{4} - 59 q^{5} - 13 q^{6} - 31 q^{7} - 31 q^{8} - 4273 q^{9} + O(q^{10}) \) \( 19824 q - 45 q^{2} - 39 q^{3} - 1915 q^{4} - 59 q^{5} - 13 q^{6} - 31 q^{7} - 31 q^{8} - 4273 q^{9} - 97 q^{10} + 57 q^{11} + 53 q^{12} - 93 q^{13} - 1476 q^{14} - 11 q^{15} - 7583 q^{16} + 137 q^{17} - 261 q^{18} + 3158 q^{19} - 259 q^{20} + 65 q^{21} + 259 q^{22} - 3623 q^{23} + 315 q^{24} - 11597 q^{25} - 37 q^{26} - 63 q^{27} + 441 q^{28} - 459 q^{29} - 5666 q^{30} + 2119 q^{31} - 259 q^{32} - 551 q^{33} + 11 q^{34} + 5465 q^{35} - 16369 q^{36} + 137 q^{37} - 305 q^{38} - 431 q^{39} - 789 q^{40} - 103 q^{41} - 11 q^{42} + 43 q^{43} + 1309 q^{44} - 39 q^{45} - 1037 q^{46} - 353 q^{47} + 709 q^{48} - 23267 q^{49} - 1977 q^{50} - 451 q^{51} - 195 q^{52} - 335 q^{53} + 619 q^{54} + 329 q^{55} + 1051 q^{56} - 436 q^{57} + 1783 q^{58} - 1235 q^{59} + 3335 q^{60} + 913 q^{61} - 1549 q^{62} + 333 q^{63} - 30511 q^{64} + 369 q^{65} + 53364 q^{66} + 321 q^{67} - 6312 q^{68} + 2325 q^{69} + 2577 q^{70} - 367 q^{71} + 40641 q^{72} - 1535 q^{73} - 1743 q^{74} + 2346 q^{75} - 5471 q^{76} - 659 q^{77} - 2218 q^{78} + 215 q^{79} - 2411 q^{80} - 39419 q^{81} + 42367 q^{82} + 1413 q^{83} - 3709 q^{84} + 25 q^{85} + 387 q^{86} + 14691 q^{87} - 1251 q^{88} - 2683 q^{89} + 52475 q^{90} + 3005 q^{91} - 1433 q^{92} - 1887 q^{93} + 22213 q^{94} - 5898 q^{95} + 1077 q^{96} - 30681 q^{97} - 4093 q^{98} - 12973 q^{99} + O(q^{100}) \)

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.