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

\( 4q + 2q^{3} - 4q^{7} + O(q^{10}) \) \( 4q + 2q^{3} - 4q^{7} - 12q^{13} - 10q^{15} - 4q^{21} + 20q^{25} + 14q^{27} + 16q^{31} + 20q^{33} - 12q^{37} - 12q^{43} - 20q^{45} - 20q^{51} - 4q^{57} - 24q^{61} + 8q^{63} - 4q^{67} + 4q^{73} + 10q^{75} + 4q^{81} + 20q^{85} + 20q^{87} + 24q^{91} + 8q^{93} + 36q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
60.2.i.a \(4\) \(0.479\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(-4\) \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)

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

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