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Properties

Label 798.4.l
Level $798$
Weight $4$
Character orbit 798.l
Rep. character $\chi_{798}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 798.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(798, [\chi])\).

Total New Old
Modular forms 976 160 816
Cusp forms 944 160 784
Eisenstein series 32 0 32

Trace form

\( 160 q - 12 q^{3} + 640 q^{4} - 32 q^{5} - 18 q^{7} - 720 q^{9} + O(q^{10}) \) \( 160 q - 12 q^{3} + 640 q^{4} - 32 q^{5} - 18 q^{7} - 720 q^{9} + 160 q^{10} - 84 q^{11} - 48 q^{12} - 150 q^{13} - 64 q^{14} + 2560 q^{16} + 252 q^{17} + 230 q^{19} - 128 q^{20} - 162 q^{21} + 128 q^{22} + 204 q^{23} + 4120 q^{25} - 304 q^{26} + 216 q^{27} - 72 q^{28} + 172 q^{29} - 24 q^{30} - 118 q^{31} + 528 q^{33} - 664 q^{34} + 196 q^{35} - 2880 q^{36} + 494 q^{37} - 72 q^{38} + 546 q^{39} + 640 q^{40} - 148 q^{41} + 24 q^{42} + 986 q^{43} - 336 q^{44} + 144 q^{45} + 824 q^{46} - 488 q^{47} - 192 q^{48} + 534 q^{49} - 224 q^{50} - 600 q^{52} - 1784 q^{53} - 404 q^{55} - 256 q^{56} - 570 q^{57} + 168 q^{58} + 2520 q^{59} - 472 q^{61} - 1072 q^{62} - 108 q^{63} + 10240 q^{64} - 88 q^{65} - 1044 q^{67} + 1008 q^{68} + 1608 q^{69} + 128 q^{70} - 336 q^{71} + 914 q^{73} + 1192 q^{74} - 2100 q^{75} + 920 q^{76} + 3396 q^{77} - 336 q^{78} + 276 q^{79} - 512 q^{80} - 6480 q^{81} + 1824 q^{82} + 6392 q^{83} - 648 q^{84} + 1448 q^{85} + 176 q^{86} + 512 q^{88} + 2920 q^{89} - 720 q^{90} - 1172 q^{91} + 816 q^{92} + 4524 q^{93} - 1416 q^{94} - 8432 q^{95} + 52 q^{97} + 656 q^{98} - 756 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(798, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(798, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)