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Properties

Label 722.6.e
Level $722$
Weight $6$
Character orbit 722.e
Rep. character $\chi_{722}(99,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $846$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 2970 846 2124
Cusp forms 2730 846 1884
Eisenstein series 240 0 240

Trace form

\( 846 q - 33 q^{3} + 12 q^{6} - 708 q^{7} + 192 q^{8} - 33 q^{9} + O(q^{10}) \) \( 846 q - 33 q^{3} + 12 q^{6} - 708 q^{7} + 192 q^{8} - 33 q^{9} - 948 q^{11} + 4272 q^{13} + 2640 q^{14} + 6366 q^{15} - 6096 q^{17} - 12648 q^{18} - 4224 q^{20} + 3996 q^{21} + 4944 q^{22} + 4476 q^{23} + 192 q^{24} + 12120 q^{25} + 1320 q^{26} - 7887 q^{27} - 6816 q^{28} + 1566 q^{29} + 6546 q^{31} - 5955 q^{33} + 9168 q^{34} - 46524 q^{35} - 528 q^{36} - 20052 q^{37} - 9528 q^{39} + 3249 q^{41} - 17712 q^{42} - 16890 q^{43} - 21504 q^{44} + 92844 q^{45} + 45600 q^{46} + 136794 q^{47} + 16896 q^{48} - 1037565 q^{49} + 90996 q^{50} - 48009 q^{51} - 3936 q^{52} - 9180 q^{53} - 138420 q^{54} - 100458 q^{55} - 66816 q^{56} - 128832 q^{58} - 292569 q^{59} + 9696 q^{60} + 87474 q^{61} + 43272 q^{62} + 358188 q^{63} - 1732608 q^{64} + 283320 q^{65} + 258612 q^{66} + 385341 q^{67} + 48720 q^{68} + 144162 q^{69} - 9168 q^{70} - 493638 q^{71} - 92544 q^{72} - 411954 q^{73} + 111240 q^{74} - 459924 q^{77} - 437928 q^{78} - 12318 q^{79} + 32469 q^{81} + 311220 q^{82} + 515652 q^{83} + 231264 q^{84} + 273264 q^{85} + 133248 q^{86} + 140616 q^{87} + 46464 q^{88} - 94464 q^{89} - 609456 q^{90} + 407580 q^{91} - 358368 q^{92} - 574278 q^{93} - 149328 q^{94} - 749811 q^{97} - 134784 q^{98} + 412095 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(722, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 2}\)