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Properties

Label 798.4.j
Level $798$
Weight $4$
Character orbit 798.j
Rep. character $\chi_{798}(457,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $144$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 976 144 832
Cusp forms 944 144 800
Eisenstein series 32 0 32

Trace form

\( 144 q - 288 q^{4} - 16 q^{5} - 48 q^{6} + 4 q^{7} - 648 q^{9} + O(q^{10}) \) \( 144 q - 288 q^{4} - 16 q^{5} - 48 q^{6} + 4 q^{7} - 648 q^{9} + 24 q^{10} + 56 q^{11} - 168 q^{15} - 1152 q^{16} - 256 q^{17} + 76 q^{19} + 128 q^{20} - 336 q^{22} - 28 q^{23} + 96 q^{24} - 1660 q^{25} + 112 q^{28} + 896 q^{29} - 76 q^{31} + 12 q^{33} - 1584 q^{35} + 5184 q^{36} - 672 q^{37} + 96 q^{40} + 1280 q^{41} - 408 q^{42} - 288 q^{43} + 224 q^{44} - 144 q^{45} + 240 q^{46} - 344 q^{47} - 1516 q^{49} - 2944 q^{50} - 552 q^{51} + 736 q^{53} + 216 q^{54} + 1568 q^{55} + 488 q^{58} + 1312 q^{59} + 336 q^{60} + 2504 q^{61} + 2784 q^{62} - 288 q^{63} + 9216 q^{64} + 200 q^{65} + 1056 q^{66} - 1048 q^{67} - 1024 q^{68} - 384 q^{69} - 1560 q^{70} + 224 q^{71} - 1160 q^{73} - 1952 q^{74} - 624 q^{75} - 608 q^{76} + 4756 q^{77} + 1056 q^{78} + 756 q^{79} - 256 q^{80} - 5832 q^{81} + 288 q^{82} - 2120 q^{83} + 3048 q^{85} - 784 q^{86} - 924 q^{87} + 672 q^{88} + 880 q^{89} - 432 q^{90} + 8848 q^{91} + 224 q^{92} + 1064 q^{95} + 384 q^{96} - 6120 q^{97} - 1120 q^{98} - 1008 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)