Properties

Label 784.6.bt
Level $784$
Weight $6$
Character orbit 784.bt
Rep. character $\chi_{784}(37,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $13392$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.bt (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(784, [\chi])\).

Total New Old
Modular forms 13488 13488 0
Cusp forms 13392 13392 0
Eisenstein series 96 96 0

Trace form

\( 13392 q - 26 q^{2} - 26 q^{3} - 26 q^{4} - 26 q^{5} - 20 q^{6} + 472 q^{8} + O(q^{10}) \) \( 13392 q - 26 q^{2} - 26 q^{3} - 26 q^{4} - 26 q^{5} - 20 q^{6} + 472 q^{8} + 508 q^{10} - 26 q^{11} - 26 q^{12} - 20 q^{13} + 2520 q^{14} - 40 q^{15} - 26 q^{16} - 52 q^{17} + 4126 q^{18} - 12 q^{19} + 7580 q^{20} + 462 q^{21} + 10036 q^{22} + 10994 q^{24} - 26 q^{26} + 952 q^{27} + 50686 q^{28} - 20 q^{29} + 52 q^{30} + 138360 q^{31} + 1884 q^{32} - 52 q^{33} + 61372 q^{34} + 8614 q^{35} + 4076 q^{36} - 26 q^{37} + 34794 q^{38} - 179966 q^{40} - 13278 q^{42} - 20 q^{43} - 20508 q^{44} + 12960 q^{45} + 25112 q^{46} + 88308 q^{47} + 98464 q^{48} - 48 q^{49} - 68452 q^{50} - 9178 q^{51} - 43256 q^{52} - 26 q^{53} + 22606 q^{54} - 619704 q^{56} - 75116 q^{58} + 14454 q^{59} + 63622 q^{60} - 26 q^{61} + 1784 q^{62} + 67180 q^{63} - 325712 q^{64} - 52 q^{65} + 857326 q^{66} + 44616 q^{67} + 8802 q^{68} + 952 q^{69} - 280388 q^{70} - 65562 q^{72} + 12096 q^{74} + 7196 q^{75} - 105170 q^{76} + 33590 q^{77} - 541984 q^{78} - 24 q^{79} - 870404 q^{80} - 7112176 q^{81} - 1006330 q^{82} + 329220 q^{83} - 1496116 q^{84} - 12520 q^{85} - 30920 q^{86} + 2024568 q^{88} + 156184 q^{90} + 368364 q^{91} + 289068 q^{92} + 2404 q^{93} + 439874 q^{94} - 38476 q^{95} - 3596724 q^{96} - 96 q^{97} + 457058 q^{98} + 235176 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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