Properties

Label 60.2.i
Level $60$
Weight $2$
Character orbit 60.i
Rep. character $\chi_{60}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
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 36 4 32
Cusp forms 12 4 8
Eisenstein series 24 0 24

Trace form

\( 4 q + 2 q^{3} - 4 q^{7} - 12 q^{13} - 10 q^{15} - 4 q^{21} + 20 q^{25} + 14 q^{27} + 16 q^{31} + 20 q^{33} - 12 q^{37} - 12 q^{43} - 20 q^{45} - 20 q^{51} - 4 q^{57} - 24 q^{61} + 8 q^{63} - 4 q^{67} + 4 q^{73}+ \cdots + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.2.i.a 60.i 15.e $4$ $0.479$ \(\Q(i, \sqrt{5})\) None 60.2.i.a \(0\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)

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

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