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Properties

Label 798.2.bc
Level $798$
Weight $2$
Character orbit 798.bc
Rep. character $\chi_{798}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $2$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
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

\( 56 q + 28 q^{4} + 12 q^{5} - 4 q^{7} + 56 q^{9} + O(q^{10}) \) \( 56 q + 28 q^{4} + 12 q^{5} - 4 q^{7} + 56 q^{9} - 12 q^{14} - 28 q^{16} + 24 q^{19} - 12 q^{21} - 24 q^{22} + 24 q^{23} + 28 q^{25} + 24 q^{26} + 4 q^{28} + 36 q^{29} + 4 q^{30} - 12 q^{34} - 20 q^{35} + 28 q^{36} - 36 q^{37} + 4 q^{39} + 12 q^{41} - 4 q^{42} - 4 q^{43} + 12 q^{45} + 12 q^{46} - 24 q^{49} + 12 q^{53} - 12 q^{55} - 4 q^{58} + 48 q^{59} - 4 q^{63} - 56 q^{64} + 72 q^{65} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 48 q^{71} + 24 q^{74} + 12 q^{76} + 56 q^{77} + 24 q^{78} - 12 q^{79} - 12 q^{80} + 56 q^{81} + 20 q^{85} - 24 q^{88} - 12 q^{91} + 12 q^{92} + 8 q^{93} - 36 q^{94} - 56 q^{95} - 48 q^{97} + 48 q^{98} + O(q^{100}) \)

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.bc.a 798.bc 133.s $28$ $6.372$ None \(0\) \(-28\) \(6\) \(4\) $\mathrm{SU}(2)[C_{6}]$
798.2.bc.b 798.bc 133.s $28$ $6.372$ None \(0\) \(28\) \(6\) \(-8\) $\mathrm{SU}(2)[C_{6}]$

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

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