# Properties

 Label 105.2.b Level $105$ Weight $2$ Character orbit 105.b Rep. character $\chi_{105}(41,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $4$ Sturm bound $32$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 105.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$32$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(105, [\chi])$$.

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

## Trace form

 $$12q - 16q^{4} - 8q^{7} - 2q^{9} + O(q^{10})$$ $$12q - 16q^{4} - 8q^{7} - 2q^{9} + 2q^{15} + 8q^{16} - 4q^{18} + 6q^{21} + 8q^{22} + 12q^{25} + 16q^{28} + 4q^{30} - 36q^{36} - 16q^{37} + 30q^{39} + 36q^{42} - 40q^{43} - 16q^{46} + 12q^{49} - 30q^{51} - 12q^{57} + 8q^{58} - 36q^{60} - 44q^{63} - 8q^{64} + 24q^{67} + 64q^{72} + 84q^{78} + 36q^{79} + 22q^{81} - 36q^{84} - 12q^{85} + 16q^{88} - 12q^{91} + 12q^{93} + 26q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.2.b.a $$2$$ $$0.838$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$4$$ $$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots$$
105.2.b.b $$2$$ $$0.838$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$4$$ $$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots$$
105.2.b.c $$4$$ $$0.838$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-1$$ $$-4$$ $$-8$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots$$
105.2.b.d $$4$$ $$0.838$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$1$$ $$4$$ $$-8$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots$$