Properties

Label 798.4.cf
Level $798$
Weight $4$
Character orbit 798.cf
Rep. character $\chi_{798}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
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.cf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
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 720 2208
Cusp forms 2832 720 2112
Eisenstein series 96 0 96

Trace form

\( 720 q - 6 q^{3} - 60 q^{6} - 30 q^{9} + O(q^{10}) \) \( 720 q - 6 q^{3} - 60 q^{6} - 30 q^{9} + 132 q^{15} - 648 q^{22} - 240 q^{24} + 1044 q^{25} + 1314 q^{27} - 1914 q^{33} - 120 q^{36} + 3648 q^{39} - 1872 q^{43} + 684 q^{45} - 1944 q^{46} - 192 q^{48} - 17640 q^{49} + 2790 q^{51} + 1944 q^{54} + 6120 q^{55} - 2784 q^{57} + 2592 q^{58} + 1056 q^{60} + 3456 q^{61} + 672 q^{63} - 23040 q^{64} - 3060 q^{66} - 4788 q^{67} - 10800 q^{69} - 3024 q^{70} - 2208 q^{72} - 4968 q^{73} + 5064 q^{78} - 1800 q^{79} + 10914 q^{81} - 7848 q^{82} + 7596 q^{85} - 2976 q^{87} - 9360 q^{90} - 2964 q^{93} + 3348 q^{97} - 15252 q^{99} + O(q^{100}) \)

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

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