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Properties

Label 65.2.o
Level $65$
Weight $2$
Character orbit 65.o
Rep. character $\chi_{65}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $20$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.o (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(65, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 20 20 0
Eisenstein series 16 16 0

Trace form

\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(65, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
65.2.o.a 65.o 65.o $20$ $0.519$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-4\) \(-2\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots\)