# Properties

 Label 91.2.c Level $91$ Weight $2$ Character orbit 91.c Rep. character $\chi_{91}(64,\cdot)$ Character field $\Q$ Dimension $6$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ 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 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

## Trace form

 $$6 q - 4 q^{4} - 2 q^{9} + O(q^{10})$$ $$6 q - 4 q^{4} - 2 q^{9} - 20 q^{12} + 8 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} + 24 q^{22} + 6 q^{23} + 8 q^{25} + 12 q^{26} - 12 q^{27} - 14 q^{29} + 16 q^{30} - 6 q^{35} + 4 q^{36} - 4 q^{38} - 8 q^{39} - 20 q^{40} - 4 q^{42} - 26 q^{43} + 8 q^{48} - 6 q^{49} + 8 q^{51} - 20 q^{52} + 2 q^{53} + 12 q^{55} + 12 q^{56} + 28 q^{61} + 16 q^{62} - 8 q^{64} - 6 q^{65} + 28 q^{66} + 20 q^{68} - 4 q^{69} - 24 q^{74} + 44 q^{75} + 16 q^{77} + 16 q^{78} + 26 q^{79} - 26 q^{81} - 56 q^{82} - 40 q^{87} - 40 q^{88} - 12 q^{90} - 2 q^{91} - 36 q^{92} + 20 q^{94} + 58 q^{95} + O(q^{100})$$

## 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.c.a $6$ $0.727$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$$