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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

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

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.