Properties

Label 60.3.g
Level $60$
Weight $3$
Character orbit 60.g
Rep. character $\chi_{60}(41,\cdot)$
Character field $\Q$
Dimension $2$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 30 2 28
Cusp forms 18 2 16
Eisenstein series 12 0 12

Trace form

\( 2q + 4q^{3} + 4q^{7} - 2q^{9} + O(q^{10}) \) \( 2q + 4q^{3} + 4q^{7} - 2q^{9} + 16q^{13} - 10q^{15} - 68q^{19} + 8q^{21} - 10q^{25} - 44q^{27} + 28q^{31} + 60q^{33} + 112q^{37} + 32q^{39} + 16q^{43} - 40q^{45} - 90q^{49} + 60q^{51} + 60q^{55} - 136q^{57} - 92q^{61} - 4q^{63} + 64q^{67} + 180q^{69} - 212q^{73} - 20q^{75} - 44q^{79} - 158q^{81} + 60q^{85} - 180q^{87} + 32q^{91} + 56q^{93} + 244q^{97} + 240q^{99} + O(q^{100}) \)

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.g.a \(2\) \(1.635\) \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(4\) \(q+(2+\beta )q^{3}+\beta q^{5}+2q^{7}+(-1+4\beta )q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)