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Properties

Label 798.4.cc
Level $798$
Weight $4$
Character orbit 798.cc
Rep. character $\chi_{798}(317,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
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.cc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
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 960 1968
Cusp forms 2832 960 1872
Eisenstein series 96 0 96

Trace form

\( 960 q + O(q^{10}) \) \( 960 q + 498 q^{13} - 384 q^{15} - 72 q^{18} - 1518 q^{19} + 216 q^{22} - 216 q^{25} + 888 q^{28} - 360 q^{34} + 756 q^{37} + 630 q^{39} + 294 q^{43} + 2736 q^{45} - 1944 q^{46} - 1152 q^{49} + 1752 q^{52} + 3528 q^{57} + 1536 q^{60} + 6564 q^{61} - 846 q^{63} - 30720 q^{64} + 816 q^{66} + 3066 q^{67} - 1584 q^{70} + 2724 q^{73} - 4272 q^{78} + 9282 q^{79} + 4608 q^{81} - 468 q^{85} + 7572 q^{87} + 5088 q^{90} - 5610 q^{91} + 1128 q^{93} - 11232 q^{94} - 3816 q^{97} + 4500 q^{99} + O(q^{100}) \)

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

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