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Properties

Label 165.2.m
Level $165$
Weight $2$
Character orbit 165.m
Rep. character $\chi_{165}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $32$
Newform subspaces $4$
Sturm bound $48$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(165, [\chi])\).

Total New Old
Modular forms 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

Trace form

\( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} - 8 q^{9} + O(q^{10}) \) \( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 4 q^{13} - 16 q^{16} - 16 q^{17} - 12 q^{18} + 8 q^{19} + 8 q^{20} - 32 q^{22} - 8 q^{23} - 36 q^{24} - 8 q^{25} + 24 q^{26} + 28 q^{28} + 8 q^{29} + 4 q^{30} + 12 q^{31} + 56 q^{32} + 4 q^{33} + 8 q^{34} + 8 q^{35} - 52 q^{37} - 36 q^{38} + 8 q^{39} + 12 q^{40} - 28 q^{41} + 32 q^{42} - 40 q^{43} + 52 q^{44} + 24 q^{46} - 32 q^{47} + 32 q^{48} - 4 q^{49} + 8 q^{50} - 4 q^{51} + 52 q^{52} + 16 q^{53} - 12 q^{55} + 8 q^{57} - 20 q^{58} + 64 q^{59} + 20 q^{61} + 16 q^{62} + 8 q^{63} - 28 q^{64} + 24 q^{65} + 20 q^{66} - 8 q^{67} - 40 q^{68} + 16 q^{69} - 28 q^{70} + 24 q^{71} + 4 q^{72} - 36 q^{73} - 84 q^{74} - 40 q^{76} - 92 q^{77} + 64 q^{78} - 32 q^{79} + 16 q^{80} - 8 q^{81} - 36 q^{82} - 4 q^{83} - 48 q^{84} + 8 q^{85} - 56 q^{86} - 88 q^{87} + 20 q^{88} - 32 q^{89} + 4 q^{90} - 12 q^{91} - 80 q^{92} + 32 q^{93} - 36 q^{94} - 12 q^{96} + 60 q^{97} + 96 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.2.m.a 165.m 11.c $8$ $1.318$ 8.0.13140625.1 None \(0\) \(-2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots\)
165.2.m.b 165.m 11.c $8$ $1.318$ 8.0.819390625.1 None \(2\) \(2\) \(2\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
165.2.m.c 165.m 11.c $8$ $1.318$ \(\Q(\zeta_{15})\) None \(2\) \(2\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
165.2.m.d 165.m 11.c $8$ $1.318$ 8.0.13140625.1 None \(4\) \(-2\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)