Properties

Label 60.7.f
Level $60$
Weight $7$
Character orbit 60.f
Rep. character $\chi_{60}(19,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(60, [\chi])\).

Total New Old
Modular forms 76 36 40
Cusp forms 68 36 32
Eisenstein series 8 0 8

Trace form

\( 36q - 66q^{4} + 44q^{5} - 162q^{6} + 8748q^{9} + O(q^{10}) \) \( 36q - 66q^{4} + 44q^{5} - 162q^{6} + 8748q^{9} - 1422q^{10} + 15484q^{14} + 1266q^{16} - 2188q^{20} - 9234q^{24} + 13812q^{25} - 32052q^{26} - 36920q^{29} - 24300q^{30} - 156204q^{34} - 16038q^{36} + 7674q^{40} + 341848q^{41} + 74892q^{44} + 10692q^{45} + 478080q^{46} + 482556q^{49} - 191448q^{50} - 39366q^{54} - 926132q^{56} + 126846q^{60} - 455976q^{61} - 618q^{64} - 624192q^{65} - 127332q^{66} - 541728q^{69} - 1871304q^{70} - 612324q^{74} - 1566456q^{76} + 2360972q^{80} + 2125764q^{81} + 858276q^{84} + 2280864q^{85} + 5157592q^{86} - 1806104q^{89} - 345546q^{90} - 3121992q^{94} - 4040118q^{96} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
60.7.f.a \(36\) \(13.803\) None \(0\) \(0\) \(44\) \(0\)

Decomposition of \(S_{7}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)