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Properties

Label 65.2.c
Level $65$
Weight $2$
Character orbit 65.c
Rep. character $\chi_{65}(51,\cdot)$
Character field $\Q$
Dimension $6$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
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 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6 q - 4 q^{3} - 10 q^{4} + 6 q^{9} + O(q^{10}) \) \( 6 q - 4 q^{3} - 10 q^{4} + 6 q^{9} + 2 q^{10} - 8 q^{13} + 8 q^{14} + 10 q^{16} + 8 q^{17} - 24 q^{22} + 16 q^{23} - 6 q^{25} + 14 q^{26} - 28 q^{27} - 4 q^{29} + 20 q^{30} - 4 q^{35} - 34 q^{36} - 20 q^{38} - 16 q^{39} - 6 q^{40} + 44 q^{42} + 24 q^{43} + 36 q^{48} + 2 q^{49} + 8 q^{51} + 20 q^{52} + 12 q^{53} - 12 q^{55} - 48 q^{56} - 12 q^{61} + 8 q^{62} + 30 q^{64} + 2 q^{65} + 24 q^{66} - 88 q^{68} - 32 q^{69} + 20 q^{74} + 4 q^{75} + 36 q^{77} - 52 q^{78} + 24 q^{79} + 30 q^{81} - 28 q^{82} - 4 q^{87} + 60 q^{88} - 34 q^{90} + 32 q^{91} - 20 q^{92} - 8 q^{94} + 16 q^{95} + O(q^{100}) \)

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.c.a 65.c 13.b $6$ $0.519$ 6.0.5089536.1 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{1})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)