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Properties

Label 798.4.k
Level $798$
Weight $4$
Character orbit 798.k
Rep. character $\chi_{798}(463,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $120$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(798, [\chi])\).

Total New Old
Modular forms 976 120 856
Cusp forms 944 120 824
Eisenstein series 32 0 32

Trace form

\( 120 q - 240 q^{4} - 540 q^{9} + O(q^{10}) \) \( 120 q - 240 q^{4} - 540 q^{9} + 192 q^{13} - 48 q^{15} - 960 q^{16} - 128 q^{17} + 32 q^{19} + 84 q^{21} + 104 q^{22} + 144 q^{23} - 1472 q^{25} + 160 q^{26} - 352 q^{29} - 48 q^{30} + 160 q^{31} + 384 q^{33} + 112 q^{35} - 2160 q^{36} - 1512 q^{37} + 688 q^{38} - 200 q^{41} + 16 q^{43} - 448 q^{46} + 328 q^{47} + 5880 q^{49} + 1088 q^{50} + 408 q^{51} + 768 q^{52} - 2512 q^{53} - 3496 q^{55} + 1464 q^{57} - 2240 q^{58} + 2512 q^{59} - 192 q^{60} - 216 q^{61} - 576 q^{62} + 7680 q^{64} + 1152 q^{65} + 240 q^{66} + 160 q^{67} + 1024 q^{68} - 2496 q^{69} + 1064 q^{70} + 1360 q^{71} - 1600 q^{73} - 464 q^{74} - 192 q^{75} + 128 q^{76} + 896 q^{77} + 624 q^{78} + 224 q^{79} - 4860 q^{81} + 320 q^{82} + 6976 q^{83} - 672 q^{84} + 4100 q^{85} + 2064 q^{86} + 2640 q^{87} - 832 q^{88} - 616 q^{89} + 728 q^{91} + 576 q^{92} + 48 q^{93} + 480 q^{94} - 10240 q^{95} - 1448 q^{97} + O(q^{100}) \)

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

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