Properties

Label 65.2.f
Level $65$
Weight $2$
Character orbit 65.f
Rep. character $\chi_{65}(18,\cdot)$
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.f (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

\( 10 q - 4 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} - 4 q^{7} + 8 q^{10} + 4 q^{11} + 10 q^{13} - 4 q^{15} - 10 q^{16} + 14 q^{17} + 18 q^{18} - 4 q^{19} - 6 q^{20} - 16 q^{21} + 8 q^{22} - 20 q^{23} + 4 q^{24}+ \cdots + 40 q^{96}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
65.2.f.a 65.f 65.f $2$ $0.519$ \(\Q(\sqrt{-1}) \) None 65.2.f.a \(0\) \(2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+i q^{2}+(-i+1)q^{3}+q^{4}+(-i-2)q^{5}+\cdots\)
65.2.f.b 65.f 65.f $8$ $0.519$ 8.0.619810816.2 None 65.2.f.b \(0\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)