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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
165.2.m.a \(8\) \(1.318\) 8.0.13140625.1 None \(0\) \(-2\) \(2\) \(1\) \(q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots\)
165.2.m.b \(8\) \(1.318\) 8.0.819390625.1 None \(2\) \(2\) \(2\) \(9\) \(q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
165.2.m.c \(8\) \(1.318\) \(\Q(\zeta_{15})\) None \(2\) \(2\) \(-2\) \(-5\) \(q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
165.2.m.d \(8\) \(1.318\) 8.0.13140625.1 None \(4\) \(-2\) \(-2\) \(3\) \(q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots\)

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

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