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Properties

Label 798.2.bx
Level $798$
Weight $2$
Character orbit 798.bx
Rep. character $\chi_{798}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $168$
Newform subspaces $2$
Sturm bound $320$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.bx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(320\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(798, [\chi])\).

Total New Old
Modular forms 1008 168 840
Cusp forms 912 168 744
Eisenstein series 96 0 96

Trace form

\( 168 q - 12 q^{7} + O(q^{10}) \) \( 168 q - 12 q^{7} - 24 q^{11} + 24 q^{14} + 24 q^{21} - 12 q^{22} + 24 q^{23} + 12 q^{25} - 72 q^{29} + 60 q^{35} + 12 q^{42} - 120 q^{43} + 24 q^{44} - 36 q^{46} + 24 q^{49} - 24 q^{53} + 12 q^{57} + 84 q^{64} + 72 q^{65} - 96 q^{67} + 48 q^{71} - 120 q^{77} + 48 q^{78} + 96 q^{79} + 132 q^{85} + 48 q^{86} - 60 q^{91} + 48 q^{92} - 72 q^{93} + 48 q^{95} - 72 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(798, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
798.2.bx.a 798.bx 133.aa $84$ $6.372$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
798.2.bx.b 798.bx 133.aa $84$ $6.372$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(798, [\chi])\) into lower level spaces

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