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Properties

Label 65.2.k
Level $65$
Weight $2$
Character orbit 65.k
Rep. character $\chi_{65}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 18 18 0
Cusp forms 10 10 0
Eisenstein series 8 8 0

Trace form

\( 10 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{6} - 6 q^{8} + O(q^{10}) \) \( 10 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{6} - 6 q^{8} - 8 q^{10} + 4 q^{11} + 4 q^{13} - 10 q^{16} - 14 q^{17} + 4 q^{19} - 20 q^{20} - 16 q^{21} + 8 q^{22} + 20 q^{23} - 4 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{27} + 16 q^{30} + 12 q^{31} + 6 q^{32} - 12 q^{33} + 2 q^{34} - 16 q^{35} - 8 q^{38} + 4 q^{39} + 28 q^{40} + 2 q^{41} + 20 q^{42} + 4 q^{43} + 12 q^{44} + 2 q^{45} + 8 q^{46} - 16 q^{48} - 18 q^{49} - 26 q^{50} - 28 q^{52} - 14 q^{53} - 12 q^{54} + 16 q^{55} - 60 q^{57} + 8 q^{59} + 44 q^{60} - 8 q^{61} + 40 q^{62} + 20 q^{63} - 34 q^{64} - 14 q^{65} - 40 q^{66} - 20 q^{67} + 2 q^{68} + 8 q^{69} + 28 q^{70} - 8 q^{71} - 24 q^{73} - 44 q^{75} + 16 q^{76} + 20 q^{77} + 40 q^{78} + 4 q^{80} - 10 q^{81} - 34 q^{82} + 20 q^{84} - 18 q^{85} - 48 q^{86} + 16 q^{87} + 16 q^{88} - 18 q^{89} + 10 q^{90} + 28 q^{91} + 44 q^{92} + 28 q^{95} + 40 q^{96} + 16 q^{97} + 98 q^{98} + O(q^{100}) \)

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.k.a 65.k 65.k $2$ $0.519$ \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(1+i)q^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
65.2.k.b 65.k 65.k $8$ $0.519$ 8.0.619810816.2 None \(-4\) \(-6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)