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Properties

Label 798.4.bx
Level $798$
Weight $4$
Character orbit 798.bx
Rep. character $\chi_{798}(13,\cdot)$
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.bx (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

\( 480 q - 24 q^{7} + O(q^{10}) \) \( 480 q - 24 q^{7} - 336 q^{11} + 48 q^{14} - 486 q^{21} - 552 q^{22} - 528 q^{23} - 276 q^{25} + 264 q^{28} - 1584 q^{29} - 708 q^{35} - 72 q^{42} + 2100 q^{43} - 672 q^{44} - 1944 q^{46} + 852 q^{49} + 1176 q^{53} + 1044 q^{57} - 108 q^{63} + 15360 q^{64} + 2520 q^{65} + 348 q^{67} + 3360 q^{70} - 2208 q^{71} - 5760 q^{74} + 2136 q^{77} - 2016 q^{78} - 912 q^{79} - 420 q^{85} - 1056 q^{86} + 3804 q^{91} - 4224 q^{92} + 2520 q^{93} + 1248 q^{95} + 5616 q^{98} + 1512 q^{99} + O(q^{100}) \)

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

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