Properties

Label 784.4.bk
Level $784$
Weight $4$
Character orbit 784.bk
Rep. character $\chi_{784}(27,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $4008$
Sturm bound $448$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bk (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 4056 4056 0
Cusp forms 4008 4008 0
Eisenstein series 48 48 0

Trace form

\( 4008q - 10q^{2} - 14q^{3} - 10q^{4} - 14q^{5} - 14q^{6} - 24q^{7} - 94q^{8} + O(q^{10}) \) \( 4008q - 10q^{2} - 14q^{3} - 10q^{4} - 14q^{5} - 14q^{6} - 24q^{7} - 94q^{8} - 14q^{10} - 10q^{11} - 14q^{12} - 14q^{13} + 108q^{14} - 10q^{16} - 28q^{17} + 84q^{18} - 14q^{20} - 66q^{21} + 494q^{22} - 20q^{23} - 14q^{24} - 14q^{26} - 14q^{27} + 142q^{28} - 10q^{29} - 56q^{30} + 970q^{32} - 28q^{33} + 994q^{34} - 490q^{35} - 266q^{36} - 10q^{37} - 14q^{38} - 20q^{39} - 1022q^{40} - 654q^{42} - 10q^{43} + 4610q^{44} - 14q^{45} - 678q^{46} - 24q^{49} - 1484q^{50} - 1518q^{51} - 14q^{52} - 10q^{53} - 14q^{54} - 28q^{55} - 1556q^{56} - 654q^{58} - 14q^{59} - 5166q^{60} - 14q^{61} - 126q^{62} + 4946q^{64} - 20q^{65} - 7714q^{66} + 1824q^{67} - 14q^{69} - 4206q^{70} - 1140q^{71} - 2058q^{72} + 2146q^{74} - 14q^{75} + 10696q^{76} + 674q^{77} - 9358q^{78} + 51496q^{81} - 12194q^{82} - 14q^{83} - 8912q^{84} - 510q^{85} + 2048q^{86} - 28q^{87} - 780q^{88} - 14q^{90} - 10650q^{91} + 2080q^{92} - 280q^{93} - 7574q^{94} - 10780q^{96} + 14300q^{98} - 3048q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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