# Properties

 Label 368.2.i Level $368$ Weight $2$ Character orbit 368.i Rep. character $\chi_{368}(91,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $92$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$368 = 2^{4} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 368.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$368$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(368, [\chi])$$.

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

## Trace form

 $$92q - 4q^{2} - 4q^{3} - 10q^{6} - 4q^{8} + O(q^{10})$$ $$92q - 4q^{2} - 4q^{3} - 10q^{6} - 4q^{8} - 10q^{12} - 4q^{13} - 16q^{16} + 24q^{18} + 4q^{23} + 4q^{24} - 24q^{26} + 20q^{27} - 20q^{29} - 24q^{32} + 16q^{35} + 38q^{36} - 32q^{39} - 16q^{46} + 56q^{48} - 76q^{49} + 8q^{50} - 72q^{52} + 52q^{54} - 8q^{55} - 74q^{58} + 8q^{59} - 2q^{62} + 42q^{64} - 24q^{69} - 12q^{70} - 8q^{71} - 66q^{72} - 12q^{75} + 40q^{77} + 34q^{78} - 68q^{81} + 66q^{82} - 16q^{85} - 8q^{87} + 4q^{92} - 16q^{93} - 60q^{94} + 24q^{96} - 88q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(368, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
368.2.i.a $$12$$ $$2.938$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-23})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{7}+\beta _{9}+\beta _{10})q^{3}+\beta _{2}q^{4}+\cdots$$
368.2.i.b $$80$$ $$2.938$$ None $$-4$$ $$-4$$ $$0$$ $$0$$