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Properties

Label 798.4.bc
Level $798$
Weight $4$
Character orbit 798.bc
Rep. character $\chi_{798}(31,\cdot)$
Character field $\Q(\zeta_{6})$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 160 q + 320 q^{4} - 48 q^{5} - 34 q^{7} + 1440 q^{9} + O(q^{10}) \) \( 160 q + 320 q^{4} - 48 q^{5} - 34 q^{7} + 1440 q^{9} + 84 q^{11} - 42 q^{13} - 24 q^{14} - 1280 q^{16} - 138 q^{19} + 198 q^{21} + 48 q^{22} - 408 q^{23} + 1868 q^{25} + 912 q^{26} - 56 q^{28} + 324 q^{29} + 24 q^{30} + 210 q^{31} + 360 q^{34} + 8 q^{35} + 2880 q^{36} + 978 q^{37} - 546 q^{39} - 444 q^{41} + 24 q^{42} - 762 q^{43} + 672 q^{44} - 432 q^{45} + 1176 q^{46} - 1018 q^{49} - 336 q^{52} - 588 q^{53} - 1068 q^{55} - 570 q^{57} - 168 q^{58} + 1968 q^{59} - 306 q^{63} - 10240 q^{64} - 576 q^{65} + 4002 q^{67} - 48 q^{68} + 1800 q^{69} + 3360 q^{70} + 2208 q^{71} + 528 q^{74} - 1368 q^{76} - 2468 q^{77} - 1008 q^{78} - 7518 q^{79} + 768 q^{80} + 12960 q^{81} - 360 q^{84} - 2456 q^{85} + 192 q^{88} + 1626 q^{91} - 816 q^{92} + 1350 q^{93} - 2904 q^{94} + 2624 q^{95} - 1332 q^{97} - 3936 q^{98} + 756 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)