Properties

Label 60.3.l
Level $60$
Weight $3$
Character orbit 60.l
Rep. character $\chi_{60}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
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 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

Trace form

\( 40q - 4q^{6} + O(q^{10}) \) \( 40q - 4q^{6} - 12q^{10} - 20q^{12} - 8q^{13} - 36q^{16} - 24q^{18} - 24q^{21} - 76q^{22} - 8q^{25} - 84q^{28} + 68q^{30} - 40q^{33} + 172q^{36} - 40q^{37} + 104q^{40} + 236q^{42} - 104q^{45} + 240q^{46} + 196q^{48} + 304q^{52} - 72q^{57} + 180q^{58} - 284q^{60} + 48q^{61} - 552q^{66} - 372q^{70} - 600q^{72} + 104q^{73} - 736q^{76} - 408q^{78} + 72q^{81} - 720q^{82} + 216q^{85} - 580q^{88} + 528q^{90} + 368q^{93} + 884q^{96} + 72q^{97} + O(q^{100}) \)

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.l.a \(40\) \(1.635\) None \(0\) \(0\) \(0\) \(0\)