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Properties

Label 722.6.g
Level $722$
Weight $6$
Character orbit 722.g
Rep. character $\chi_{722}(39,\cdot)$
Character field $\Q(\zeta_{19})$
Dimension $2826$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 722.g (of order \(19\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 361 \)
Character field: \(\Q(\zeta_{19})\)
Sturm bound: \(570\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(722, [\chi])\).

Total New Old
Modular forms 8586 2826 5760
Cusp forms 8514 2826 5688
Eisenstein series 72 0 72

Trace form

\( 2826 q - 4 q^{2} - 205 q^{3} - 2512 q^{4} - 8 q^{6} - 312 q^{7} - 64 q^{8} - 12580 q^{9} + O(q^{10}) \) \( 2826 q - 4 q^{2} - 205 q^{3} - 2512 q^{4} - 8 q^{6} - 312 q^{7} - 64 q^{8} - 12580 q^{9} - 200 q^{10} - 478 q^{11} + 64 q^{12} - 1338 q^{13} - 8440 q^{14} - 1868 q^{15} - 40192 q^{16} + 482 q^{17} - 628 q^{18} + 361 q^{19} + 2940 q^{21} - 21224 q^{22} + 2792 q^{23} - 128 q^{24} - 85629 q^{25} + 2144 q^{26} + 46487 q^{27} - 4992 q^{28} - 48318 q^{29} + 71176 q^{30} + 11164 q^{31} - 1024 q^{32} - 21244 q^{33} - 3080 q^{34} + 11312 q^{35} - 197936 q^{36} - 10038 q^{37} + 113848 q^{38} - 12236 q^{39} - 3200 q^{40} - 25722 q^{41} - 8608 q^{42} + 27742 q^{43} - 7648 q^{44} + 357390 q^{45} + 112552 q^{46} - 295702 q^{47} + 1024 q^{48} - 585313 q^{49} + 43316 q^{50} - 47816 q^{51} - 21408 q^{52} - 53370 q^{53} + 1936 q^{54} - 87012 q^{55} - 135040 q^{56} + 6498 q^{57} + 36112 q^{58} + 31028 q^{59} - 29888 q^{60} - 72400 q^{61} + 46192 q^{62} - 124846 q^{63} - 643072 q^{64} + 721616 q^{65} + 50496 q^{66} + 29516 q^{67} + 27168 q^{68} - 871212 q^{69} + 554320 q^{70} - 5892 q^{71} - 10048 q^{72} + 31946 q^{73} + 298760 q^{74} - 396786 q^{75} - 37392 q^{76} + 63016 q^{77} + 2800 q^{78} - 202780 q^{79} - 633806 q^{81} - 225512 q^{82} + 568169 q^{83} + 47040 q^{84} + 27556 q^{85} + 345560 q^{86} - 1583554 q^{87} + 22784 q^{88} - 430560 q^{89} - 85720 q^{90} + 460854 q^{91} + 44672 q^{92} - 353832 q^{93} + 791560 q^{94} - 797810 q^{95} - 2048 q^{96} - 882904 q^{97} - 243076 q^{98} - 388226 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(722, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(722, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(722, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 2}\)