Properties

Label 441.4.bh
Level $441$
Weight $4$
Character orbit 441.bh
Rep. character $\chi_{441}(20,\cdot)$
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.bh (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

\( 1992q - 15q^{2} - 14q^{3} - 661q^{4} - 21q^{5} - 70q^{6} - 12q^{7} - 80q^{9} + O(q^{10}) \) \( 1992q - 15q^{2} - 14q^{3} - 661q^{4} - 21q^{5} - 70q^{6} - 12q^{7} - 80q^{9} - 28q^{10} - 15q^{11} - 399q^{12} - 7q^{13} + 300q^{14} - 148q^{15} + 2539q^{16} + 174q^{18} - 21q^{20} + 43q^{21} + 27q^{22} - 645q^{23} - 14q^{24} + 3945q^{25} - 56q^{27} - 328q^{28} + 615q^{29} - 310q^{30} - 399q^{32} - 14q^{33} - 7q^{34} - 458q^{36} + 820q^{37} + 147q^{38} + 744q^{39} - 7q^{40} - 21q^{41} - 4204q^{42} + 163q^{43} + 1750q^{45} + 2532q^{46} + 1365q^{47} + 72q^{49} - 1458q^{50} - 350q^{51} - 1351q^{52} - 14q^{54} + 4256q^{55} - 1233q^{56} - 3772q^{57} - 1233q^{58} - 21q^{59} - 1584q^{60} + 2933q^{61} - 797q^{63} + 19212q^{64} - 2367q^{65} + 5502q^{66} + 576q^{67} + 10906q^{69} - 391q^{70} - 3024q^{72} - 28q^{73} + 2553q^{74} + 11074q^{75} + 441q^{76} + 2766q^{77} + 2394q^{78} - 180q^{79} - 9796q^{81} - 28q^{82} - 21q^{83} + 4682q^{84} + 245q^{85} + 8301q^{86} - 742q^{87} - 1301q^{88} - 2408q^{90} - 238q^{91} - 15885q^{92} - 7397q^{93} - 7q^{94} - 1668q^{95} + 23191q^{96} - 19762q^{99} + O(q^{100}) \)

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

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