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Properties

Label 441.4.bd
Level $441$
Weight $4$
Character orbit 441.bd
Rep. character $\chi_{441}(47,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1992$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.bd (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

Total New Old
Modular forms 2040 2040 0
Cusp forms 1992 1992 0
Eisenstein series 48 48 0

Trace form

\( 1992 q - 18 q^{2} - 11 q^{3} - 664 q^{4} - 15 q^{5} + 38 q^{6} - 12 q^{7} + 169 q^{9} + O(q^{10}) \) \( 1992 q - 18 q^{2} - 11 q^{3} - 664 q^{4} - 15 q^{5} + 38 q^{6} - 12 q^{7} + 169 q^{9} - 22 q^{10} - 21 q^{11} - 396 q^{12} - 43 q^{13} - 150 q^{14} + 59 q^{15} + 2560 q^{16} - 72 q^{17} + 24 q^{18} - 36 q^{19} + 3 q^{20} + 292 q^{21} - 21 q^{22} + 861 q^{23} + 52 q^{24} - 7905 q^{25} - 96 q^{26} + 376 q^{27} + 128 q^{28} - 771 q^{29} - 7 q^{30} - 198 q^{31} - 210 q^{32} - 863 q^{33} + 17 q^{34} + 765 q^{35} + 298 q^{36} + 1066 q^{37} + 1725 q^{38} + 531 q^{39} - 7 q^{40} + 597 q^{41} + 5261 q^{42} - 89 q^{43} + 795 q^{44} + 1447 q^{45} + 3234 q^{46} + 180 q^{47} - 1569 q^{48} - 522 q^{49} + 675 q^{50} - 263 q^{51} - 1351 q^{52} + 1092 q^{53} + 670 q^{54} - 2170 q^{55} - 3621 q^{56} + 1871 q^{57} - 1233 q^{58} - 768 q^{59} - 6912 q^{60} - 4678 q^{61} - 3072 q^{62} - 1571 q^{63} + 19548 q^{64} - 1194 q^{65} - 525 q^{66} - 288 q^{67} - 7050 q^{68} - 6479 q^{69} + 383 q^{70} + 9702 q^{71} - 315 q^{72} - 22 q^{73} - 21 q^{74} - 2384 q^{75} + 297 q^{76} + 1182 q^{77} + 8991 q^{78} + 90 q^{79} - 4239 q^{80} + 7505 q^{81} - 46 q^{82} + 1809 q^{83} + 23489 q^{84} - 130 q^{85} - 21 q^{86} + 1388 q^{87} - 1253 q^{88} - 10014 q^{89} + 7585 q^{90} + 1112 q^{91} + 21885 q^{92} - 13700 q^{93} - 4 q^{94} - 3657 q^{95} + 391 q^{96} - 792 q^{97} + 5667 q^{98} + 9845 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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