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Properties

Label 798.4.bu
Level $798$
Weight $4$
Character orbit 798.bu
Rep. character $\chi_{798}(53,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
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.bu (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
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 960 1968
Cusp forms 2832 960 1872
Eisenstein series 96 0 96

Trace form

\( 960 q + O(q^{10}) \) \( 960 q + 498 q^{13} - 384 q^{15} + 72 q^{18} + 1272 q^{19} + 216 q^{22} + 108 q^{25} - 120 q^{28} - 360 q^{34} - 756 q^{37} + 630 q^{39} + 294 q^{43} - 1368 q^{45} + 2304 q^{49} - 1992 q^{52} + 3528 q^{57} - 1488 q^{60} - 6972 q^{61} + 1692 q^{63} - 30720 q^{64} + 816 q^{66} - 4368 q^{67} + 3168 q^{70} - 4314 q^{73} - 4272 q^{78} - 7098 q^{79} - 6336 q^{81} + 864 q^{84} - 468 q^{85} - 15144 q^{87} + 5088 q^{90} - 1398 q^{91} - 7188 q^{93} + 11232 q^{94} - 3816 q^{97} + 4500 q^{99} + O(q^{100}) \)

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

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