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Properties

Label 798.4.bo
Level $798$
Weight $4$
Character orbit 798.bo
Rep. character $\chi_{798}(43,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $360$
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.bo (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
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 360 2568
Cusp forms 2832 360 2472
Eisenstein series 96 0 96

Trace form

\( 360 q + O(q^{10}) \) \( 360 q - 288 q^{15} - 768 q^{17} + 216 q^{22} + 624 q^{23} + 1644 q^{25} + 96 q^{29} + 120 q^{31} - 1152 q^{33} - 336 q^{35} - 1776 q^{37} - 624 q^{38} - 1200 q^{41} - 1872 q^{43} + 2856 q^{46} + 2832 q^{47} - 8820 q^{49} + 3744 q^{53} - 936 q^{55} - 1044 q^{57} - 2592 q^{58} - 2640 q^{59} + 576 q^{60} - 3456 q^{61} - 96 q^{62} - 11520 q^{64} + 2640 q^{67} + 3024 q^{70} - 4824 q^{71} - 2280 q^{73} + 1392 q^{74} + 9840 q^{79} + 7536 q^{82} + 2280 q^{83} + 1008 q^{84} - 6036 q^{85} - 7776 q^{86} + 1368 q^{87} + 2112 q^{88} - 11976 q^{89} - 4416 q^{92} - 11472 q^{95} - 14664 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)