# Properties

 Label 91.2.i Level $91$ Weight $2$ Character orbit 91.i Rep. character $\chi_{91}(34,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 91.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(91, [\chi])$$.

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

## Trace form

 $$12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} + O(q^{10})$$ $$12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(91, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
91.2.i.a $$12$$ $$0.727$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-4$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{8}q^{2}+\beta _{10}q^{3}+(-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$$