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Properties

Label 806.2.k
Level $806$
Weight $2$
Character orbit 806.k
Rep. character $\chi_{806}(157,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $128$
Newform subspaces $5$
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.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
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 464 128 336
Cusp forms 432 128 304
Eisenstein series 32 0 32

Trace form

\( 128 q + 8 q^{3} - 32 q^{4} + 8 q^{5} - 16 q^{6} - 12 q^{7} - 24 q^{9} + O(q^{10}) \) \( 128 q + 8 q^{3} - 32 q^{4} + 8 q^{5} - 16 q^{6} - 12 q^{7} - 24 q^{9} + 8 q^{10} + 4 q^{11} + 8 q^{12} + 2 q^{13} - 6 q^{14} + 4 q^{15} - 32 q^{16} - 6 q^{17} + 8 q^{20} + 32 q^{21} + 8 q^{22} + 20 q^{23} + 4 q^{24} + 184 q^{25} - 24 q^{26} - 82 q^{27} + 8 q^{28} - 12 q^{29} + 28 q^{30} - 68 q^{31} - 44 q^{33} + 8 q^{34} + 12 q^{35} + 136 q^{36} - 80 q^{37} + 8 q^{38} - 12 q^{40} + 8 q^{41} + 40 q^{43} + 4 q^{44} + 20 q^{45} + 32 q^{46} - 36 q^{47} - 12 q^{48} - 74 q^{49} - 8 q^{50} - 66 q^{51} + 2 q^{52} - 60 q^{53} + 16 q^{54} + 40 q^{55} + 4 q^{56} + 16 q^{57} + 12 q^{58} - 12 q^{59} + 4 q^{60} - 44 q^{61} + 24 q^{62} + 88 q^{63} - 32 q^{64} - 4 q^{65} + 32 q^{66} - 8 q^{67} + 4 q^{68} + 64 q^{69} + 32 q^{70} + 24 q^{71} - 52 q^{73} + 20 q^{74} - 30 q^{75} - 22 q^{77} + 72 q^{79} - 12 q^{80} - 28 q^{81} + 8 q^{82} + 12 q^{83} + 32 q^{84} - 48 q^{85} + 44 q^{86} - 40 q^{87} - 52 q^{88} + 60 q^{89} - 12 q^{90} + 4 q^{91} + 40 q^{92} - 60 q^{93} - 4 q^{94} - 80 q^{95} + 4 q^{96} - 20 q^{97} - 160 q^{98} + 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.k.a 806.k 31.d $4$ $6.436$ \(\Q(\zeta_{10})\) None \(-1\) \(4\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots\)
806.2.k.b 806.k 31.d $20$ $6.436$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-5\) \(-1\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{9}q^{2}+\beta _{8}q^{3}+(-1-\beta _{5}-\beta _{9}+\cdots)q^{4}+\cdots\)
806.2.k.c 806.k 31.d $28$ $6.436$ None \(7\) \(1\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$
806.2.k.d 806.k 31.d $36$ $6.436$ None \(9\) \(1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$
806.2.k.e 806.k 31.d $40$ $6.436$ None \(-10\) \(3\) \(14\) \(-7\) $\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)