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

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