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Properties

Label 798.4.b
Level $798$
Weight $4$
Character orbit 798.b
Rep. character $\chi_{798}(113,\cdot)$
Character field $\Q$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 488 120 368
Cusp forms 472 120 352
Eisenstein series 16 0 16

Trace form

\( 120 q + 480 q^{4} + 40 q^{6} + 20 q^{9} + O(q^{10}) \) \( 120 q + 480 q^{4} + 40 q^{6} + 20 q^{9} + 1920 q^{16} - 228 q^{19} + 160 q^{24} - 2544 q^{25} - 896 q^{30} + 80 q^{36} - 968 q^{39} + 2616 q^{43} + 2856 q^{45} + 5880 q^{49} + 1240 q^{54} + 2928 q^{55} + 1184 q^{57} + 432 q^{58} + 1512 q^{61} + 1288 q^{63} + 7680 q^{64} + 2800 q^{66} - 1584 q^{73} - 912 q^{76} - 260 q^{81} + 5376 q^{82} - 6432 q^{85} + 952 q^{87} - 8776 q^{93} + 640 q^{96} - 10024 q^{99} + O(q^{100}) \)

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

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