# Properties

 Label 1849.4.a Level $1849$ Weight $4$ Character orbit 1849.a Rep. character $\chi_{1849}(1,\cdot)$ Character field $\Q$ Dimension $431$ Newform subspaces $13$ Sturm bound $630$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1849 = 43^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1849.a (trivial) Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$630$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(1849))$$.

Total New Old
Modular forms 495 472 23
Cusp forms 451 431 20
Eisenstein series 44 41 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$43$$Dim.
$$+$$$$221$$
$$-$$$$210$$

## Trace form

 $$431q - 2q^{2} + 4q^{3} + 1656q^{4} - 16q^{5} + 30q^{6} + 12q^{7} + 12q^{8} + 3519q^{9} + O(q^{10})$$ $$431q - 2q^{2} + 4q^{3} + 1656q^{4} - 16q^{5} + 30q^{6} + 12q^{7} + 12q^{8} + 3519q^{9} - 54q^{10} + 80q^{11} + 96q^{12} - 58q^{13} + 72q^{14} + 32q^{15} + 5900q^{16} + 196q^{17} - 218q^{18} - 24q^{19} - 216q^{20} + 108q^{21} + 302q^{22} - 2q^{23} + 358q^{24} + 8921q^{25} + 6q^{26} - 20q^{27} + 484q^{28} - 416q^{29} + 96q^{30} - 318q^{31} - 216q^{32} - 508q^{33} + 54q^{34} + 176q^{35} + 12402q^{36} + 180q^{37} + 82q^{38} - 388q^{39} - 746q^{40} + 100q^{41} + 32q^{42} + 990q^{44} + 4q^{45} - 994q^{46} - 558q^{47} + 752q^{48} + 14849q^{49} - 1934q^{50} - 408q^{51} - 280q^{52} + 886q^{53} - 822q^{54} + 372q^{55} - 222q^{56} + 768q^{57} + 1826q^{58} - 1152q^{59} + 2398q^{60} + 956q^{61} - 1506q^{62} + 376q^{63} + 17916q^{64} + 412q^{65} - 1206q^{66} + 680q^{67} + 1254q^{68} + 2368q^{69} + 2620q^{70} - 324q^{71} - 252q^{72} - 1492q^{73} - 1504q^{74} + 2432q^{75} - 2676q^{76} - 616q^{77} - 2132q^{78} + 778q^{79} - 2368q^{80} + 20159q^{81} + 614q^{82} + 1868q^{83} - 2630q^{84} + 68q^{85} - 814q^{87} - 1208q^{88} - 2640q^{89} + 392q^{90} + 3048q^{91} - 558q^{92} - 1844q^{93} - 964q^{94} - 1660q^{95} + 3164q^{96} + 1340q^{97} - 4050q^{98} + 1220q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(1849))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 43
1849.4.a.a $$1$$ $$109.095$$ $$\Q$$ $$\Q(\sqrt{-43})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q-8q^{4}-3^{3}q^{9}+2^{5}q^{11}-90q^{13}+\cdots$$
1849.4.a.b $$4$$ $$109.095$$ 4.4.45868.1 None $$4$$ $$11$$ $$27$$ $$20$$ $$-$$ $$q+(1-\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots$$
1849.4.a.c $$6$$ $$109.095$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-6$$ $$-7$$ $$-43$$ $$-8$$ $$-$$ $$q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots$$
1849.4.a.d $$10$$ $$109.095$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-1$$ $$5$$ $$19$$ $$51$$ $$+$$ $$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(2-\beta _{7}+\cdots)q^{5}+\cdots$$
1849.4.a.e $$10$$ $$109.095$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{7}+\beta _{9})q^{4}+\cdots$$
1849.4.a.f $$10$$ $$109.095$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$1$$ $$-5$$ $$-19$$ $$-51$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$$
1849.4.a.g $$30$$ $$109.095$$ None $$-6$$ $$-2$$ $$-27$$ $$-48$$ $$-$$
1849.4.a.h $$30$$ $$109.095$$ None $$6$$ $$2$$ $$27$$ $$48$$ $$+$$
1849.4.a.i $$50$$ $$109.095$$ None $$-10$$ $$-2$$ $$8$$ $$-6$$ $$-$$
1849.4.a.j $$50$$ $$109.095$$ None $$10$$ $$2$$ $$-8$$ $$6$$ $$-$$
1849.4.a.k $$60$$ $$109.095$$ None $$-15$$ $$-37$$ $$-51$$ $$-54$$ $$-$$
1849.4.a.l $$60$$ $$109.095$$ None $$15$$ $$37$$ $$51$$ $$54$$ $$+$$
1849.4.a.m $$110$$ $$109.095$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(1849))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(1849)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(43))$$$$^{\oplus 2}$$