# Properties

 Label 276.2.c Level $276$ Weight $2$ Character orbit 276.c Rep. character $\chi_{276}(47,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $2$ Sturm bound $96$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 276.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(276, [\chi])$$.

Total New Old
Modular forms 52 44 8
Cusp forms 44 44 0
Eisenstein series 8 0 8

## Trace form

 $$44q - 3q^{6} - 4q^{9} + O(q^{10})$$ $$44q - 3q^{6} - 4q^{9} + 8q^{10} + 7q^{12} - 8q^{13} + 8q^{16} - q^{18} + 4q^{22} - 8q^{24} - 36q^{25} + 12q^{28} + 10q^{30} - 16q^{33} - 12q^{34} - 33q^{36} - 8q^{37} - 8q^{40} - 12q^{42} - 5q^{48} - 28q^{49} - 38q^{52} - 32q^{54} + 24q^{57} + 6q^{58} + 36q^{60} + 24q^{61} + 6q^{64} + 42q^{66} + 12q^{72} - 8q^{73} + 52q^{76} - 35q^{78} + 20q^{81} - 58q^{82} + 38q^{84} + 16q^{85} - 60q^{88} + 58q^{90} + 24q^{93} - 26q^{94} - 27q^{96} - 8q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(276, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
276.2.c.a $$22$$ $$2.204$$ None $$0$$ $$0$$ $$0$$ $$0$$
276.2.c.b $$22$$ $$2.204$$ None $$0$$ $$0$$ $$0$$ $$0$$