# Properties

 Label 605.2.g Level $605$ Weight $2$ Character orbit 605.g Rep. character $\chi_{605}(81,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $144$ Newform subspaces $17$ Sturm bound $132$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 605.g (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$17$$ Sturm bound: $$132$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

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

Total New Old
Modular forms 312 144 168
Cusp forms 216 144 72
Eisenstein series 96 0 96

## Trace form

 $$144q + 6q^{2} + 4q^{3} - 32q^{4} - 6q^{6} + 4q^{7} - 2q^{8} - 30q^{9} + O(q^{10})$$ $$144q + 6q^{2} + 4q^{3} - 32q^{4} - 6q^{6} + 4q^{7} - 2q^{8} - 30q^{9} - 8q^{10} + 12q^{12} - 2q^{13} + 4q^{14} - 6q^{15} - 20q^{16} + 12q^{17} - 14q^{18} - 14q^{19} + 8q^{20} + 32q^{21} - 8q^{23} - 38q^{24} - 36q^{25} + 12q^{26} - 20q^{27} + 2q^{28} - 10q^{29} + 20q^{30} + 8q^{31} - 28q^{32} - 32q^{34} + 12q^{35} - 26q^{36} - 20q^{37} + 30q^{38} - 30q^{39} + 6q^{40} - 4q^{41} - 10q^{42} - 4q^{43} + 38q^{46} + 4q^{47} + 34q^{48} - 14q^{49} + 6q^{50} - 14q^{51} + 54q^{52} - 12q^{53} + 24q^{54} - 180q^{56} + 50q^{57} + 6q^{58} + 58q^{59} - 26q^{60} - 4q^{61} + 68q^{62} - 26q^{63} - 12q^{64} - 16q^{65} + 24q^{67} - 46q^{68} + 30q^{69} - 28q^{70} - 8q^{71} + 64q^{72} + 10q^{73} - 68q^{74} - 6q^{75} - 16q^{76} - 140q^{78} - 54q^{79} - 8q^{80} - 32q^{81} - 22q^{82} - 2q^{83} - 24q^{84} + 16q^{85} + 58q^{86} - 68q^{87} - 48q^{89} + 26q^{90} - 96q^{91} - 60q^{92} - 8q^{93} - 50q^{94} + 16q^{95} - 6q^{96} - 88q^{97} + 68q^{98} + O(q^{100})$$

## 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.g.a $$4$$ $$4.831$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
605.2.g.b $$4$$ $$4.831$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$3$$ $$-1$$ $$-3$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
605.2.g.c $$4$$ $$4.831$$ $$\Q(\zeta_{10})$$ None $$1$$ $$0$$ $$-1$$ $$0$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots$$
605.2.g.d $$4$$ $$4.831$$ $$\Q(\zeta_{10})$$ None $$1$$ $$3$$ $$-1$$ $$3$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots$$
605.2.g.e $$8$$ $$4.831$$ 8.0.13140625.1 None $$-3$$ $$5$$ $$2$$ $$-4$$ $$q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$$
605.2.g.f $$8$$ $$4.831$$ 8.0.64000000.2 None $$-2$$ $$0$$ $$2$$ $$4$$ $$q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots$$
605.2.g.g $$8$$ $$4.831$$ 8.0.159390625.1 None $$-1$$ $$1$$ $$-2$$ $$8$$ $$q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$$
605.2.g.h $$8$$ $$4.831$$ 8.0.324000000.3 None $$0$$ $$-4$$ $$-2$$ $$0$$ $$q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$$
605.2.g.i $$8$$ $$4.831$$ 8.0.324000000.3 None $$0$$ $$2$$ $$2$$ $$0$$ $$q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$$
605.2.g.j $$8$$ $$4.831$$ 8.0.159390625.1 None $$1$$ $$1$$ $$-2$$ $$-8$$ $$q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$$
605.2.g.k $$8$$ $$4.831$$ 8.0.13140625.1 None $$2$$ $$-5$$ $$2$$ $$1$$ $$q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$$
605.2.g.l $$8$$ $$4.831$$ 8.0.64000000.2 None $$2$$ $$0$$ $$2$$ $$-4$$ $$q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$$
605.2.g.m $$8$$ $$4.831$$ 8.0.13140625.1 None $$3$$ $$5$$ $$2$$ $$4$$ $$q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$$
605.2.g.n $$8$$ $$4.831$$ 8.0.159390625.1 None $$4$$ $$1$$ $$-2$$ $$3$$ $$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$$
605.2.g.o $$12$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-1$$ $$-1$$ $$3$$ $$1$$ $$q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$$
605.2.g.p $$12$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$1$$ $$-1$$ $$3$$ $$-1$$ $$q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots$$
605.2.g.q $$24$$ $$4.831$$ None $$0$$ $$-6$$ $$-6$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(605, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$