# Properties

 Label 354.2.c Level 354 Weight 2 Character orbit c Rep. character $$\chi_{354}(353,\cdot)$$ Character field $$\Q$$ Dimension 20 Newforms 2 Sturm bound 120 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$354 = 2 \cdot 3 \cdot 59$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 354.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$177$$ Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$120$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(354, [\chi])$$.

Total New Old
Modular forms 64 20 44
Cusp forms 56 20 36
Eisenstein series 8 0 8

## Trace form

 $$20q - 2q^{3} + 20q^{4} - 4q^{7} + 6q^{9} + O(q^{10})$$ $$20q - 2q^{3} + 20q^{4} - 4q^{7} + 6q^{9} - 2q^{12} - 14q^{15} + 20q^{16} - 12q^{19} - 6q^{21} - 8q^{22} + 8q^{25} - 20q^{27} - 4q^{28} + 6q^{36} - 22q^{45} + 16q^{46} - 2q^{48} + 16q^{49} + 4q^{51} - 6q^{57} - 14q^{60} - 38q^{63} + 20q^{64} - 8q^{75} - 12q^{76} + 8q^{78} + 12q^{79} + 14q^{81} - 6q^{84} - 8q^{85} - 30q^{87} - 8q^{88} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(354, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
354.2.c.a $$10$$ $$2.827$$ 10.0.$$\cdots$$.1 None $$-10$$ $$-1$$ $$0$$ $$-2$$ $$q-q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots$$
354.2.c.b $$10$$ $$2.827$$ 10.0.$$\cdots$$.1 None $$10$$ $$-1$$ $$0$$ $$-2$$ $$q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{6}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(354, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(354, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(177, [\chi])$$$$^{\oplus 2}$$