Properties

Label 806.2.n
Level $806$
Weight $2$
Character orbit 806.n
Rep. character $\chi_{806}(621,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 806.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).

Total New Old
Modular forms 232 72 160
Cusp forms 216 72 144
Eisenstein series 16 0 16

Trace form

\( 72 q + 36 q^{4} - 32 q^{9} + O(q^{10}) \) \( 72 q + 36 q^{4} - 32 q^{9} + 12 q^{11} - 12 q^{13} + 8 q^{14} - 36 q^{16} - 12 q^{19} + 8 q^{23} - 72 q^{25} + 4 q^{26} + 24 q^{27} - 8 q^{30} - 12 q^{33} - 32 q^{35} + 32 q^{36} + 12 q^{37} - 24 q^{38} + 8 q^{39} - 12 q^{41} - 12 q^{42} + 8 q^{43} - 60 q^{45} + 32 q^{49} - 16 q^{51} - 32 q^{53} + 36 q^{54} + 4 q^{55} + 4 q^{56} - 12 q^{58} - 12 q^{59} + 8 q^{61} + 8 q^{62} + 60 q^{63} - 72 q^{64} + 8 q^{65} + 16 q^{66} + 24 q^{67} + 40 q^{69} + 12 q^{71} - 24 q^{72} + 4 q^{74} + 24 q^{75} - 12 q^{76} + 40 q^{77} + 8 q^{78} - 16 q^{79} - 12 q^{81} + 24 q^{84} - 48 q^{85} + 52 q^{87} + 24 q^{89} - 16 q^{90} + 16 q^{92} - 12 q^{94} - 8 q^{95} + 24 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
806.2.n.a 806.n 13.e $28$ $6.436$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
806.2.n.b 806.n 13.e $44$ $6.436$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)