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Properties

Label 66.2.h
Level $66$
Weight $2$
Character orbit 66.h
Rep. character $\chi_{66}(17,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
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.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 16 48
Cusp forms 32 16 16
Eisenstein series 32 0 32

Trace form

\( 16 q + 4 q^{3} - 4 q^{4} - 5 q^{6} - 16 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{3} - 4 q^{4} - 5 q^{6} - 16 q^{9} - 6 q^{12} - 12 q^{15} - 4 q^{16} - 5 q^{18} - 30 q^{19} + 12 q^{22} + 5 q^{24} - 12 q^{25} + 10 q^{27} + 10 q^{28} + 30 q^{30} + 26 q^{31} + 37 q^{33} + 20 q^{34} + 9 q^{36} + 12 q^{37} + 10 q^{39} + 10 q^{40} - 4 q^{42} - 16 q^{45} - 20 q^{46} + 4 q^{48} - 36 q^{49} - 15 q^{51} - 20 q^{52} - 28 q^{55} + 35 q^{57} - 46 q^{58} + 8 q^{60} - 20 q^{61} + 10 q^{63} - 4 q^{64} - 52 q^{66} - 4 q^{67} - 2 q^{69} - 34 q^{70} - 20 q^{72} + 10 q^{73} - 33 q^{75} - 16 q^{78} + 20 q^{79} - 12 q^{81} + 6 q^{82} + 60 q^{85} + 12 q^{88} + 10 q^{90} + 48 q^{91} - 26 q^{93} + 80 q^{94} + 18 q^{97} + 46 q^{99} + O(q^{100}) \)

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.h.a 66.h 33.f $8$ $0.527$ 8.0.185640625.1 None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
66.2.h.b 66.h 33.f $8$ $0.527$ 8.0.185640625.1 None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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