Properties

Label 60.2.j
Level $60$
Weight $2$
Character orbit 60.j
Rep. character $\chi_{60}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 60.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
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 32 12 20
Cusp forms 16 12 4
Eisenstein series 16 0 16

Trace form

\( 12q - 4q^{6} - 12q^{8} + O(q^{10}) \) \( 12q - 4q^{6} - 12q^{8} - 8q^{10} - 8q^{12} - 4q^{13} + 12q^{16} - 20q^{17} + 20q^{20} + 12q^{22} - 20q^{25} + 16q^{26} - 4q^{28} + 8q^{30} + 20q^{32} + 8q^{33} + 4q^{36} + 4q^{37} + 16q^{38} - 8q^{40} + 16q^{41} + 20q^{42} + 4q^{45} - 40q^{46} + 16q^{48} - 16q^{50} - 8q^{52} + 4q^{53} - 64q^{56} - 20q^{58} - 20q^{60} - 32q^{61} - 56q^{62} + 20q^{65} - 24q^{66} - 16q^{68} + 44q^{70} - 12q^{72} + 44q^{73} + 8q^{76} + 48q^{77} - 24q^{78} + 4q^{80} - 12q^{81} + 16q^{82} + 44q^{85} + 64q^{86} + 60q^{88} + 12q^{90} + 56q^{92} - 16q^{93} + 44q^{96} - 20q^{97} + 24q^{98} + O(q^{100}) \)

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.j.a \(12\) \(0.479\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{4}-\beta _{7})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)