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Properties

Label 798.4.ca
Level $798$
Weight $4$
Character orbit 798.ca
Rep. character $\chi_{798}(325,\cdot)$
Character field $\Q(\zeta_{18})$
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.ca (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 480 q - 24 q^{7} + O(q^{10}) \) \( 480 q - 24 q^{7} + 168 q^{11} + 144 q^{12} - 54 q^{13} - 24 q^{14} - 36 q^{17} - 486 q^{19} + 18 q^{21} - 48 q^{22} - 528 q^{23} - 600 q^{25} + 1368 q^{26} - 324 q^{27} - 312 q^{28} + 936 q^{29} - 1080 q^{34} + 1524 q^{35} - 756 q^{37} + 1332 q^{41} - 72 q^{42} - 294 q^{43} + 336 q^{44} + 1944 q^{46} + 852 q^{49} + 72 q^{52} + 1176 q^{53} - 1440 q^{56} + 1044 q^{57} - 2952 q^{59} + 360 q^{61} + 702 q^{63} + 15360 q^{64} + 3750 q^{67} - 1968 q^{70} - 2208 q^{71} + 1296 q^{73} - 5760 q^{74} + 6300 q^{75} - 2448 q^{76} + 7140 q^{77} + 1008 q^{78} - 8778 q^{79} - 6228 q^{83} + 1092 q^{85} + 528 q^{86} + 4506 q^{91} - 4224 q^{92} + 5670 q^{93} + 2808 q^{94} - 2496 q^{95} - 1728 q^{97} - 6192 q^{98} - 756 q^{99} + O(q^{100}) \)

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

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