# Properties

 Label 430.2.q Level 430 Weight 2 Character orbit q Rep. character $$\chi_{430}(31,\cdot)$$ Character field $$\Q(\zeta_{21})$$ Dimension 192 Newform subspaces 4 Sturm bound 132 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$430 = 2 \cdot 5 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 430.q (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$43$$ Character field: $$\Q(\zeta_{21})$$ Newform subspaces: $$4$$ Sturm bound: $$132$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(430, [\chi])$$.

Total New Old
Modular forms 840 192 648
Cusp forms 744 192 552
Eisenstein series 96 0 96

## Trace form

 $$192q + 4q^{2} - 4q^{3} - 32q^{4} - 2q^{5} - 2q^{6} - 8q^{7} + 4q^{8} + 32q^{9} + O(q^{10})$$ $$192q + 4q^{2} - 4q^{3} - 32q^{4} - 2q^{5} - 2q^{6} - 8q^{7} + 4q^{8} + 32q^{9} + 4q^{11} - 4q^{12} + 10q^{14} - 32q^{16} - 2q^{17} - 10q^{18} + 52q^{19} - 2q^{20} - 8q^{21} + 38q^{22} + 16q^{23} + 12q^{24} + 16q^{25} + 20q^{26} + 32q^{27} - 8q^{28} + 6q^{29} - 2q^{30} + 36q^{31} + 4q^{32} + 18q^{33} - 66q^{34} - 8q^{35} - 122q^{36} - 40q^{37} + 38q^{38} - 104q^{39} - 24q^{41} - 112q^{42} + 54q^{43} - 52q^{44} + 48q^{45} - 108q^{46} - 40q^{47} - 4q^{48} - 152q^{49} + 12q^{50} - 2q^{51} - 56q^{52} + 4q^{53} - 56q^{54} - 8q^{55} - 4q^{56} + 88q^{57} - 28q^{58} + 96q^{59} + 36q^{61} - 12q^{62} + 104q^{63} - 32q^{64} + 8q^{65} + 52q^{66} + 42q^{67} - 2q^{68} - 8q^{69} + 32q^{70} - 16q^{71} - 10q^{72} - 102q^{73} + 48q^{74} - 20q^{75} + 10q^{76} + 12q^{77} + 72q^{78} + 20q^{79} + 12q^{80} - 144q^{81} + 20q^{82} - 78q^{83} - 8q^{84} - 56q^{85} + 128q^{86} + 168q^{87} + 38q^{88} - 8q^{89} - 16q^{90} - 52q^{91} + 16q^{92} - 12q^{93} + 36q^{94} - 44q^{95} - 2q^{96} + 72q^{97} + 46q^{98} + 38q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(430, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
430.2.q.a $$36$$ $$3.434$$ None $$-6$$ $$5$$ $$3$$ $$1$$
430.2.q.b $$48$$ $$3.434$$ None $$-8$$ $$-1$$ $$-4$$ $$-7$$
430.2.q.c $$48$$ $$3.434$$ None $$8$$ $$-7$$ $$4$$ $$-3$$
430.2.q.d $$60$$ $$3.434$$ None $$10$$ $$-1$$ $$-5$$ $$1$$

## Decomposition of $$S_{2}^{\mathrm{old}}(430, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(430, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(43, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(86, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(215, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database