Properties

Label 441.4.z
Level $441$
Weight $4$
Character orbit 441.z
Rep. character $\chi_{441}(4,\cdot)$
Character field $\Q(\zeta_{21})$
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.z (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
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

\( 1992q - 8q^{2} - 13q^{3} + 648q^{4} - 45q^{5} - 22q^{6} - 4q^{8} - 195q^{9} + O(q^{10}) \) \( 1992q - 8q^{2} - 13q^{3} + 648q^{4} - 45q^{5} - 22q^{6} - 4q^{8} - 195q^{9} - 10q^{10} - 5q^{11} - 358q^{12} + 7q^{13} - 278q^{14} - 25q^{15} + 2544q^{16} + 134q^{17} - 148q^{18} - 72q^{19} + 355q^{20} - 180q^{21} + 11q^{22} + 205q^{23} - 428q^{24} - 7905q^{25} + 238q^{26} - 328q^{27} + 144q^{28} - 341q^{29} - 315q^{30} - 54q^{31} + 386q^{32} - 37q^{33} - 13q^{34} - 317q^{35} + 1490q^{36} - 1118q^{37} - 1417q^{38} + 283q^{39} - 43q^{40} + 685q^{41} - 353q^{42} + 79q^{43} + 479q^{44} - 15q^{45} - 3286q^{46} + 74q^{47} + 985q^{48} + 270q^{49} - 9q^{50} + 1137q^{51} + 667q^{52} + 1850q^{53} - 924q^{54} - 1300q^{55} - 7721q^{56} + 1581q^{57} - 1297q^{58} + 1658q^{59} + 6340q^{60} + 5434q^{61} - 1896q^{62} - 507q^{63} - 19332q^{64} + 634q^{65} + 4095q^{66} - 288q^{67} + 20086q^{68} - 6863q^{69} + 1037q^{70} - 2890q^{71} - 667q^{72} + 310q^{73} + 411q^{74} + 5208q^{75} - 1461q^{76} + 2902q^{77} + 5217q^{78} + 342q^{79} - 10877q^{80} + 20497q^{81} - 34q^{82} + 1153q^{83} - 8711q^{84} - 130q^{85} - 4713q^{86} - 2060q^{87} + 731q^{88} - 2588q^{89} - 285q^{90} - 1580q^{91} - 9853q^{92} + 8242q^{93} + 1184q^{94} - 1445q^{95} - 15717q^{96} + 252q^{97} + 9027q^{98} - 7513q^{99} + O(q^{100}) \)

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

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