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Properties

Label 798.2.i
Level $798$
Weight $2$
Character orbit 798.i
Rep. character $\chi_{798}(163,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $4$
Sturm bound $320$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(320\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 336 56 280
Cusp forms 304 56 248
Eisenstein series 32 0 32

Trace form

\( 56 q - 28 q^{4} - 4 q^{5} + 4 q^{7} + 56 q^{9} + O(q^{10}) \) \( 56 q - 28 q^{4} - 4 q^{5} + 4 q^{7} + 56 q^{9} + 8 q^{10} + 8 q^{13} - 20 q^{14} - 28 q^{16} - 24 q^{17} - 8 q^{19} + 8 q^{20} - 4 q^{21} + 24 q^{23} - 52 q^{25} - 8 q^{26} + 4 q^{28} - 4 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 20 q^{34} + 20 q^{35} - 28 q^{36} - 20 q^{37} + 24 q^{38} - 4 q^{39} + 8 q^{40} + 4 q^{41} - 4 q^{42} + 12 q^{43} - 4 q^{45} + 12 q^{46} + 8 q^{47} + 24 q^{49} - 16 q^{50} - 16 q^{52} + 20 q^{53} + 4 q^{55} + 16 q^{56} + 4 q^{58} - 48 q^{59} - 8 q^{61} - 8 q^{62} + 4 q^{63} + 56 q^{64} - 32 q^{65} - 24 q^{67} + 12 q^{68} - 40 q^{69} - 16 q^{70} + 40 q^{73} + 8 q^{74} + 4 q^{76} - 48 q^{77} + 8 q^{78} - 44 q^{79} - 4 q^{80} + 56 q^{81} - 32 q^{82} + 16 q^{83} + 8 q^{84} - 12 q^{85} + 16 q^{86} + 128 q^{89} + 8 q^{90} + 44 q^{91} - 12 q^{92} + 8 q^{93} + 36 q^{94} - 40 q^{95} + 16 q^{97} - 32 q^{98} + O(q^{100}) \)

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.i.a 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-7\) \(-14\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{8})q^{2}-q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
798.2.i.b 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-7\) \(14\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+q^{3}+\beta _{3}q^{4}-\beta _{1}q^{5}+\cdots\)
798.2.i.c 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(7\) \(-14\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
798.2.i.d 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(7\) \(14\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{6})q^{2}+q^{3}-\beta _{6}q^{4}-\beta _{7}q^{5}+\cdots\)

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

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