# Properties

 Label 19.4.a Level $19$ Weight $4$ Character orbit 19.a Rep. character $\chi_{19}(1,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $6$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$19$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 19.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$6$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(19))$$.

Total New Old
Modular forms 6 4 2
Cusp forms 4 4 0
Eisenstein series 2 0 2

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

$$19$$Dim
$$+$$$$3$$
$$-$$$$1$$

## Trace form

 $$4 q - 4 q^{3} + 22 q^{4} + 2 q^{5} - 50 q^{6} - 24 q^{7} + 48 q^{8} + 46 q^{9} + O(q^{10})$$ $$4 q - 4 q^{3} + 22 q^{4} + 2 q^{5} - 50 q^{6} - 24 q^{7} + 48 q^{8} + 46 q^{9} - 52 q^{10} - 38 q^{11} - 120 q^{12} + 76 q^{13} + 4 q^{14} + 200 q^{15} - 38 q^{16} - 64 q^{17} + 144 q^{18} - 38 q^{19} + 88 q^{20} - 80 q^{21} + 280 q^{22} + 82 q^{23} - 594 q^{24} - 18 q^{25} + 266 q^{26} - 232 q^{27} - 482 q^{28} + 128 q^{29} - 556 q^{30} - 84 q^{31} + 624 q^{32} + 140 q^{33} + 608 q^{34} - 570 q^{35} + 1072 q^{36} - 540 q^{37} - 114 q^{38} - 426 q^{39} - 324 q^{40} + 1196 q^{41} + 1550 q^{42} - 766 q^{43} + 56 q^{44} + 254 q^{45} - 788 q^{46} - 102 q^{47} - 1056 q^{48} - 320 q^{49} - 1696 q^{50} + 652 q^{51} + 708 q^{52} + 1252 q^{53} - 1382 q^{54} + 450 q^{55} - 684 q^{56} - 114 q^{57} + 1394 q^{58} + 460 q^{59} + 1420 q^{60} + 630 q^{61} - 1604 q^{62} - 1326 q^{63} + 274 q^{64} - 372 q^{65} - 1084 q^{66} - 1168 q^{67} - 1622 q^{68} - 108 q^{69} + 2436 q^{70} + 600 q^{71} + 2784 q^{72} + 980 q^{73} - 20 q^{74} + 1936 q^{75} - 380 q^{76} - 506 q^{77} - 1652 q^{78} + 348 q^{79} - 620 q^{80} - 1172 q^{81} + 152 q^{82} - 532 q^{83} + 852 q^{84} - 126 q^{85} + 3180 q^{86} - 426 q^{87} - 792 q^{88} - 340 q^{89} - 1960 q^{90} - 336 q^{91} - 2494 q^{92} + 612 q^{93} + 408 q^{94} - 494 q^{95} + 638 q^{96} - 1692 q^{97} - 1784 q^{98} + 358 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(19))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 19
19.4.a.a $1$ $1.121$ $$\Q$$ None $$-3$$ $$-5$$ $$-12$$ $$11$$ $-$ $$q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots$$
19.4.a.b $3$ $1.121$ 3.3.3144.1 None $$3$$ $$1$$ $$14$$ $$-35$$ $+$ $$q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots$$