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Properties

Label 798.2.ca
Level $798$
Weight $2$
Character orbit 798.ca
Rep. character $\chi_{798}(325,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $156$
Newform subspaces $2$
Sturm bound $320$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.ca (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: \(1\)
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 156 852
Cusp forms 912 156 756
Eisenstein series 96 0 96

Trace form

\( 156 q - 12 q^{7} + O(q^{10}) \) \( 156 q - 12 q^{7} + 12 q^{11} + 6 q^{12} + 6 q^{13} - 12 q^{14} + 36 q^{17} + 48 q^{19} - 18 q^{21} + 24 q^{22} + 24 q^{23} + 48 q^{25} + 36 q^{26} - 6 q^{27} + 36 q^{34} - 12 q^{35} + 36 q^{37} - 36 q^{41} + 12 q^{42} + 18 q^{43} - 12 q^{44} + 36 q^{46} + 24 q^{49} + 12 q^{52} - 24 q^{53} + 36 q^{56} + 12 q^{57} - 72 q^{59} - 6 q^{61} + 78 q^{64} - 18 q^{67} - 72 q^{70} + 48 q^{71} + 6 q^{73} + 42 q^{75} - 36 q^{76} - 48 q^{77} - 24 q^{78} - 18 q^{79} - 36 q^{83} + 60 q^{85} - 24 q^{86} + 90 q^{91} + 48 q^{92} + 84 q^{93} - 36 q^{94} - 96 q^{95} + 108 q^{97} + 72 q^{98} + 12 q^{99} + O(q^{100}) \)

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.ca.a 798.ca 133.ab $72$ $6.372$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
798.2.ca.b 798.ca 133.ab $84$ $6.372$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$

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

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