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Properties

Label 798.4.bj
Level $798$
Weight $4$
Character orbit 798.bj
Rep. character $\chi_{798}(559,\cdot)$
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.bj (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

\( 160 q + 320 q^{4} + 44 q^{7} - 720 q^{9} + O(q^{10}) \) \( 160 q + 320 q^{4} + 44 q^{7} - 720 q^{9} + 336 q^{11} + 24 q^{14} - 1280 q^{16} - 18 q^{21} + 552 q^{22} + 120 q^{23} + 2540 q^{25} + 88 q^{28} - 936 q^{29} - 48 q^{30} - 736 q^{35} + 2880 q^{36} - 504 q^{39} + 24 q^{42} - 804 q^{43} + 672 q^{44} + 2468 q^{49} - 1176 q^{53} - 276 q^{57} - 672 q^{58} - 198 q^{63} - 10240 q^{64} - 4884 q^{67} - 3360 q^{70} + 2208 q^{71} + 1920 q^{74} - 6008 q^{77} + 2016 q^{78} + 6132 q^{79} - 6480 q^{81} - 356 q^{85} - 528 q^{86} + 7014 q^{91} - 480 q^{92} - 372 q^{93} - 8128 q^{95} + 6192 q^{98} - 1512 q^{99} + O(q^{100}) \)

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

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