Properties

Label 666.2.h
Level $666$
Weight $2$
Character orbit 666.h
Rep. character $\chi_{666}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $76$
Newform subspaces $3$
Sturm bound $228$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(228\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

Total New Old
Modular forms 236 76 160
Cusp forms 220 76 144
Eisenstein series 16 0 16

Trace form

\( 76 q - 4 q^{3} + 76 q^{4} - 8 q^{5} + 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 76 q - 4 q^{3} + 76 q^{4} - 8 q^{5} + 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{15} + 76 q^{16} - 4 q^{19} - 8 q^{20} + 6 q^{21} + 16 q^{23} + 52 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{28} - 6 q^{29} - 12 q^{30} + 14 q^{31} + 32 q^{33} - 6 q^{35} - 4 q^{36} + 10 q^{37} - 12 q^{38} + 20 q^{39} + 24 q^{41} + 2 q^{42} + 2 q^{43} - 4 q^{44} - 28 q^{45} + 4 q^{47} - 4 q^{48} - 36 q^{49} - 32 q^{50} - 22 q^{51} - 4 q^{52} - 14 q^{53} + 12 q^{54} + 12 q^{55} + 2 q^{57} - 34 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{62} + 14 q^{63} + 76 q^{64} + 32 q^{65} - 16 q^{67} - 26 q^{69} - 18 q^{71} - 28 q^{73} + 14 q^{74} - 70 q^{75} - 4 q^{76} - 40 q^{77} + 18 q^{78} + 2 q^{79} - 8 q^{80} + 4 q^{81} - 24 q^{82} - 16 q^{83} + 6 q^{84} + 12 q^{85} - 4 q^{86} + 6 q^{87} + 32 q^{89} + 76 q^{90} + 10 q^{91} + 16 q^{92} + 66 q^{93} - 2 q^{95} + 8 q^{97} - 8 q^{98} + 44 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
666.2.h.a 666.h 333.h $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+2q^{5}+\cdots\)
666.2.h.b 666.h 333.h $36$ $5.318$ None \(-36\) \(-2\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{3}]$
666.2.h.c 666.h 333.h $38$ $5.318$ None \(38\) \(-2\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)