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Properties

Label 66.2.e
Level $66$
Weight $2$
Character orbit 66.e
Rep. character $\chi_{66}(25,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $8$
Newform subspaces $2$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 66.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(66, [\chi])\).

Total New Old
Modular forms 64 8 56
Cusp forms 32 8 24
Eisenstein series 32 0 32

Trace form

\( 8 q - 2 q^{4} + 8 q^{5} + 2 q^{6} - 8 q^{7} - 2 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{4} + 8 q^{5} + 2 q^{6} - 8 q^{7} - 2 q^{9} - 12 q^{10} - 8 q^{11} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 16 q^{17} + 20 q^{19} + 8 q^{20} - 16 q^{21} + 10 q^{22} + 2 q^{24} - 14 q^{25} + 12 q^{26} + 2 q^{28} - 12 q^{29} + 12 q^{30} + 2 q^{31} + 10 q^{33} - 8 q^{34} + 28 q^{35} - 2 q^{36} + 24 q^{37} + 12 q^{38} + 8 q^{39} - 2 q^{40} + 20 q^{41} - 2 q^{42} - 32 q^{43} - 8 q^{44} + 8 q^{45} + 12 q^{46} - 12 q^{47} + 14 q^{49} - 24 q^{50} - 12 q^{51} - 12 q^{53} - 8 q^{54} - 8 q^{55} + 16 q^{56} - 12 q^{57} + 10 q^{58} - 12 q^{59} - 8 q^{60} - 4 q^{61} - 12 q^{62} - 8 q^{63} - 2 q^{64} - 8 q^{65} - 12 q^{66} - 16 q^{68} + 8 q^{69} - 22 q^{70} - 4 q^{71} - 6 q^{73} - 16 q^{74} + 24 q^{75} + 8 q^{77} - 20 q^{79} - 12 q^{80} - 2 q^{81} + 12 q^{82} + 28 q^{83} + 4 q^{84} - 24 q^{85} - 16 q^{86} + 20 q^{87} - 10 q^{88} + 16 q^{89} + 8 q^{90} + 24 q^{91} + 20 q^{92} + 12 q^{93} + 16 q^{94} + 52 q^{95} + 2 q^{96} + 20 q^{97} + 48 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(66, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
66.2.e.a 66.e 11.c $4$ $0.527$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(8\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
66.2.e.b 66.e 11.c $4$ $0.527$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(66, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(66, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)