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Properties

Label 798.4.bq
Level $798$
Weight $4$
Character orbit 798.bq
Rep. character $\chi_{798}(25,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $480$
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.bq (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 2928 480 2448
Cusp forms 2832 480 2352
Eisenstein series 96 0 96

Trace form

\( 480 q - 48 q^{7} + O(q^{10}) \) \( 480 q - 48 q^{7} + 336 q^{11} + 210 q^{13} + 24 q^{14} - 24 q^{17} + 552 q^{19} - 384 q^{20} - 378 q^{21} - 384 q^{22} + 1056 q^{23} + 660 q^{25} - 912 q^{26} + 168 q^{28} + 744 q^{29} + 360 q^{34} - 2304 q^{35} - 252 q^{37} + 444 q^{41} - 72 q^{42} - 378 q^{43} - 672 q^{44} + 432 q^{45} + 1296 q^{46} + 2856 q^{49} + 840 q^{52} + 588 q^{53} + 480 q^{56} + 1044 q^{57} + 1968 q^{59} - 912 q^{61} + 3216 q^{62} + 378 q^{63} - 15360 q^{64} + 420 q^{65} + 7920 q^{67} + 3072 q^{68} - 3312 q^{69} + 4944 q^{70} - 2208 q^{71} - 294 q^{73} + 600 q^{74} - 816 q^{76} - 3804 q^{77} + 1008 q^{78} + 990 q^{79} - 2076 q^{83} - 84 q^{85} - 528 q^{86} + 8328 q^{89} - 9738 q^{91} + 4224 q^{92} - 1134 q^{93} - 9960 q^{94} + 1248 q^{95} + 4392 q^{97} + 576 q^{98} + 756 q^{99} + O(q^{100}) \)

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

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