Properties

Label 60.3.c
Level $60$
Weight $3$
Character orbit 60.c
Rep. character $\chi_{60}(31,\cdot)$
Character field $\Q$
Dimension $8$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
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 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8q + 4q^{2} + 10q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q + 4q^{2} + 10q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + 10q^{10} + 16q^{13} - 20q^{14} + 34q^{16} - 12q^{18} - 40q^{20} - 48q^{21} + 68q^{22} + 18q^{24} + 40q^{25} - 36q^{26} + 28q^{28} + 64q^{29} - 76q^{32} - 92q^{34} - 30q^{36} - 112q^{37} - 40q^{38} - 10q^{40} - 16q^{41} + 108q^{42} + 172q^{44} + 152q^{46} + 48q^{48} - 56q^{49} + 20q^{50} - 128q^{52} + 352q^{53} + 18q^{54} + 116q^{56} + 144q^{57} - 204q^{58} + 30q^{60} - 176q^{61} - 56q^{62} - 110q^{64} - 80q^{65} + 108q^{66} - 184q^{68} - 96q^{69} - 60q^{70} + 60q^{72} - 240q^{73} + 132q^{74} - 24q^{76} - 288q^{77} - 240q^{78} - 80q^{80} + 72q^{81} + 40q^{82} - 36q^{84} + 160q^{85} - 200q^{86} + 140q^{88} + 80q^{89} - 30q^{90} + 144q^{92} + 144q^{93} - 96q^{94} - 174q^{96} + 432q^{97} + 660q^{98} + O(q^{100}) \)

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.c.a \(8\) \(1.635\) 8.0.85100625.1 None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)