Properties

Label 60.3.f
Level $60$
Weight $3$
Character orbit 60.f
Rep. character $\chi_{60}(19,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 28 12 16
Cusp forms 20 12 8
Eisenstein series 8 0 8

Trace form

\( 12q - 2q^{4} + 4q^{5} + 6q^{6} + 36q^{9} + O(q^{10}) \) \( 12q - 2q^{4} + 4q^{5} + 6q^{6} + 36q^{9} - 22q^{10} - 52q^{14} - 78q^{16} + 52q^{20} - 18q^{24} - 68q^{25} + 156q^{26} - 40q^{29} - 60q^{30} - 28q^{34} - 6q^{36} + 154q^{40} - 184q^{41} + 204q^{44} + 12q^{45} + 160q^{46} + 212q^{49} + 72q^{50} + 18q^{54} - 244q^{56} + 126q^{60} + 8q^{61} - 266q^{64} - 192q^{65} - 84q^{66} - 96q^{69} - 104q^{70} - 468q^{74} + 168q^{76} - 308q^{80} + 108q^{81} - 348q^{84} + 224q^{85} - 136q^{86} + 632q^{89} - 66q^{90} + 376q^{94} + 234q^{96} + O(q^{100}) \)

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.f.a \(4\) \(1.635\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
60.3.f.b \(8\) \(1.635\) 8.0.\(\cdots\).4 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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