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Properties

Label 798.4.bp
Level $798$
Weight $4$
Character orbit 798.bp
Rep. character $\chi_{798}(289,\cdot)$
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.bp (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

\( 480 q + 24 q^{7} + O(q^{10}) \) \( 480 q + 24 q^{7} - 168 q^{11} + 210 q^{13} + 24 q^{14} + 12 q^{17} - 78 q^{19} - 384 q^{20} - 18 q^{21} - 384 q^{22} - 528 q^{23} - 168 q^{25} + 456 q^{26} + 312 q^{28} + 744 q^{29} + 360 q^{34} + 36 q^{35} - 252 q^{37} + 444 q^{41} - 72 q^{42} - 378 q^{43} + 336 q^{44} - 864 q^{45} - 648 q^{46} - 1428 q^{49} - 1176 q^{52} - 1176 q^{53} + 480 q^{56} + 1044 q^{57} - 984 q^{59} + 3084 q^{61} + 3216 q^{62} + 702 q^{63} - 15360 q^{64} - 840 q^{65} - 1818 q^{67} - 6144 q^{68} - 3312 q^{69} - 5136 q^{70} - 2208 q^{71} - 420 q^{73} + 2976 q^{74} - 816 q^{76} - 3804 q^{77} + 1008 q^{78} + 6714 q^{79} - 2076 q^{83} - 84 q^{85} - 528 q^{86} - 312 q^{89} - 6678 q^{91} + 4224 q^{92} - 5670 q^{93} - 9960 q^{94} - 2496 q^{95} + 4392 q^{97} - 6192 q^{98} + 756 q^{99} + O(q^{100}) \)

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

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