↑

Properties

Label 798.4.cg
Level $798$
Weight $4$
Character orbit 798.cg
Rep. character $\chi_{798}(251,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
Sturm bound $640$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 798.cg (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

\( 960 q + O(q^{10}) \) \( 960 q - 636 q^{15} + 48 q^{18} + 216 q^{22} - 108 q^{25} + 552 q^{28} + 1008 q^{37} - 2520 q^{39} - 924 q^{43} + 648 q^{46} - 1152 q^{49} + 6384 q^{57} + 960 q^{60} + 846 q^{63} + 30720 q^{64} + 6468 q^{67} + 1584 q^{70} + 4272 q^{78} - 11928 q^{79} - 4416 q^{81} - 288 q^{84} - 36 q^{85} - 12 q^{91} - 14376 q^{93} - 20712 q^{99} + O(q^{100}) \)

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

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