# Properties

 Label 2960.1.fm Level $2960$ Weight $1$ Character orbit 2960.fm Rep. character $\chi_{2960}(1157,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $4$ Newform subspaces $1$ Sturm bound $456$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2960 = 2^{4} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2960.fm (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2960$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$456$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2960, [\chi])$$.

Total New Old
Modular forms 20 20 0
Cusp forms 4 4 0
Eisenstein series 16 16 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 0 0 4 0

## Trace form

 $$4 q + 2 q^{4} + 4 q^{6} - 2 q^{7} + O(q^{10})$$ $$4 q + 2 q^{4} + 4 q^{6} - 2 q^{7} - 4 q^{10} + 4 q^{11} - 4 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{21} - 2 q^{22} + 4 q^{23} + 2 q^{24} + 2 q^{25} - 4 q^{26} + 2 q^{28} - 4 q^{31} + 2 q^{33} + 2 q^{35} - 2 q^{39} - 2 q^{40} - 2 q^{42} - 4 q^{43} + 2 q^{44} - 2 q^{46} - 2 q^{53} - 2 q^{54} - 2 q^{55} - 2 q^{56} + 2 q^{59} - 4 q^{60} + 2 q^{61} - 4 q^{64} + 2 q^{65} + 4 q^{66} + 2 q^{69} + 2 q^{70} + 4 q^{74} - 4 q^{77} + 2 q^{81} + 4 q^{82} - 4 q^{84} - 4 q^{88} + 2 q^{91} + 2 q^{92} - 2 q^{96} + 2 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2960, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2960.1.fm.a $$4$$ $$1.477$$ $$\Q(\zeta_{12})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$$