Properties

Label 60.2.d
Level $60$
Weight $2$
Character orbit 60.d
Rep. character $\chi_{60}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 60.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(60, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

Trace form

\( 2 q + 2 q^{5} - 2 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{5} - 2 q^{9} - 8 q^{11} - 4 q^{15} + 8 q^{21} - 6 q^{25} + 12 q^{29} + 8 q^{31} + 16 q^{35} - 20 q^{41} - 2 q^{45} - 18 q^{49} + 8 q^{51} - 8 q^{55} - 8 q^{59} + 4 q^{61} - 8 q^{69} - 8 q^{75} + 24 q^{79} + 2 q^{81} + 16 q^{85} + 20 q^{89} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.2.d.a 60.d 5.b $2$ $0.479$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1+2i)q^{5}-4iq^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)