Properties

Label 60.3.k
Level $60$
Weight $3$
Character orbit 60.k
Rep. character $\chi_{60}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(60, [\chi])\).

Total New Old
Modular forms 60 4 56
Cusp forms 36 4 32
Eisenstein series 24 0 24

Trace form

\( 4q + 12q^{5} + 20q^{7} + O(q^{10}) \) \( 4q + 12q^{5} + 20q^{7} - 16q^{11} - 24q^{15} - 40q^{17} - 24q^{21} - 40q^{23} - 16q^{25} + 16q^{31} + 60q^{33} + 56q^{35} + 200q^{41} + 120q^{43} - 12q^{45} - 24q^{51} - 200q^{53} - 108q^{55} + 120q^{57} - 312q^{61} + 60q^{63} + 240q^{65} - 40q^{67} - 80q^{71} - 20q^{73} - 168q^{75} - 200q^{77} - 36q^{81} - 240q^{83} - 184q^{85} + 60q^{87} + 240q^{91} + 120q^{93} + 400q^{95} + 300q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
60.3.k.a \(4\) \(1.635\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(12\) \(20\) \(q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)