Properties

Label 806.2.bk
Level $806$
Weight $2$
Character orbit 806.bk
Rep. character $\chi_{806}(131,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $256$
Newform subspaces $4$
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.bk (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 4 \)
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 928 256 672
Cusp forms 864 256 608
Eisenstein series 64 0 64

Trace form

\( 256 q - 8 q^{3} - 64 q^{4} + 4 q^{5} + 16 q^{6} + 24 q^{7} + 24 q^{9} + O(q^{10}) \) \( 256 q - 8 q^{3} - 64 q^{4} + 4 q^{5} + 16 q^{6} + 24 q^{7} + 24 q^{9} - 8 q^{10} - 4 q^{11} - 8 q^{12} - 2 q^{13} + 12 q^{14} + 20 q^{15} - 64 q^{16} + 6 q^{17} + 4 q^{20} + 4 q^{21} - 26 q^{22} - 20 q^{23} - 4 q^{24} - 124 q^{25} + 24 q^{26} - 2 q^{27} + 4 q^{28} - 60 q^{29} + 8 q^{30} - 28 q^{31} - 4 q^{33} - 8 q^{34} - 60 q^{35} - 136 q^{36} - 40 q^{37} + 10 q^{38} + 12 q^{40} + 52 q^{41} - 30 q^{42} + 20 q^{43} - 4 q^{44} + 40 q^{45} + 16 q^{46} + 36 q^{47} + 12 q^{48} + 62 q^{49} + 56 q^{50} + 18 q^{51} - 2 q^{52} + 78 q^{53} + 32 q^{54} - 40 q^{55} + 2 q^{56} + 56 q^{57} + 24 q^{59} + 20 q^{60} + 92 q^{61} + 12 q^{62} - 16 q^{63} - 64 q^{64} + 4 q^{65} - 32 q^{66} - 4 q^{67} - 4 q^{68} + 8 q^{69} - 32 q^{70} + 12 q^{71} + 76 q^{73} + 16 q^{74} - 78 q^{75} - 104 q^{77} - 12 q^{79} - 36 q^{80} - 92 q^{81} - 56 q^{82} + 96 q^{83} + 4 q^{84} - 24 q^{85} - 8 q^{86} - 80 q^{87} - 26 q^{88} + 60 q^{89} - 174 q^{90} + 8 q^{91} - 40 q^{92} - 252 q^{93} - 56 q^{94} - 208 q^{95} - 4 q^{96} + 44 q^{97} - 128 q^{98} + 48 q^{99} + O(q^{100}) \)

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.bk.a 806.bk 31.g $48$ $6.436$ None \(-12\) \(-3\) \(9\) \(-7\) $\mathrm{SU}(2)[C_{15}]$
806.2.bk.b 806.bk 31.g $56$ $6.436$ None \(14\) \(-1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{15}]$
806.2.bk.c 806.bk 31.g $72$ $6.436$ None \(18\) \(-1\) \(5\) \(17\) $\mathrm{SU}(2)[C_{15}]$
806.2.bk.d 806.bk 31.g $80$ $6.436$ None \(-20\) \(-3\) \(-11\) \(10\) $\mathrm{SU}(2)[C_{15}]$

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

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