# Properties

 Label 605.2.j Level $605$ Weight $2$ Character orbit 605.j Rep. character $\chi_{605}(9,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $184$ Newform subspaces $11$ Sturm bound $132$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 605.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$11$$ Sturm bound: $$132$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$2$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(605, [\chi])$$.

Total New Old
Modular forms 312 248 64
Cusp forms 216 184 32
Eisenstein series 96 64 32

## Trace form

 $$184q + 44q^{4} + 3q^{5} + 18q^{6} + 26q^{9} + O(q^{10})$$ $$184q + 44q^{4} + 3q^{5} + 18q^{6} + 26q^{9} + 16q^{14} + 13q^{15} - 40q^{16} - 6q^{19} + 4q^{20} - 8q^{21} - 6q^{24} + 13q^{25} - 84q^{26} - 2q^{29} - 26q^{30} - 2q^{31} - 80q^{34} - 22q^{35} - 2q^{36} - 30q^{39} - 12q^{40} + 52q^{41} - 84q^{45} + 62q^{46} - 28q^{50} + 42q^{51} + 40q^{54} - 12q^{56} + 4q^{59} + 90q^{60} + 40q^{61} - 28q^{64} + 40q^{65} - 36q^{69} + 18q^{70} - 54q^{71} - 48q^{74} - 21q^{75} - 56q^{76} - 38q^{79} + 16q^{80} - 42q^{81} - 12q^{84} - 58q^{85} - 6q^{86} - 144q^{89} - 78q^{90} + 28q^{91} - 14q^{94} - 48q^{95} + 86q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(605, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
605.2.j.a $$8$$ $$4.831$$ 8.0.484000000.6 $$\Q(\sqrt{-55})$$ $$0$$ $$0$$ $$-10$$ $$0$$ $$q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots$$
605.2.j.b $$8$$ $$4.831$$ 8.0.228765625.1 $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots$$
605.2.j.c $$8$$ $$4.831$$ 8.0.484000000.6 $$\Q(\sqrt{-55})$$ $$0$$ $$0$$ $$10$$ $$0$$ $$q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots$$
605.2.j.d $$16$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots$$
605.2.j.e $$16$$ $$4.831$$ 16.0.$$\cdots$$.7 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$$
605.2.j.f $$16$$ $$4.831$$ 16.0.$$\cdots$$.7 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$$
605.2.j.g $$16$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{13}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$$
605.2.j.h $$16$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{13}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$$
605.2.j.i $$16$$ $$4.831$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(\beta _{1}+\beta _{4}+\beta _{5}-\beta _{8}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots$$
605.2.j.j $$16$$ $$4.831$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(\beta _{1}+\beta _{4}+\beta _{5}-\beta _{8}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots$$
605.2.j.k $$48$$ $$4.831$$ None $$0$$ $$0$$ $$6$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(605, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(605, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$