Properties

 Label 38.4.a Level $38$ Weight $4$ Character orbit 38.a Rep. character $\chi_{38}(1,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $3$ Sturm bound $20$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$38 = 2 \cdot 19$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 38.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$20$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(38))$$.

Total New Old
Modular forms 17 5 12
Cusp forms 13 5 8
Eisenstein series 4 0 4

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

$$2$$$$19$$FrickeDim
$$+$$$$+$$$$+$$$$2$$
$$+$$$$-$$$$-$$$$1$$
$$-$$$$-$$$$+$$$$2$$
Plus space$$+$$$$4$$
Minus space$$-$$$$1$$

Trace form

 $$5 q - 2 q^{2} + 8 q^{3} + 20 q^{4} - 8 q^{5} + 20 q^{6} + 8 q^{7} - 8 q^{8} + 35 q^{9} + O(q^{10})$$ $$5 q - 2 q^{2} + 8 q^{3} + 20 q^{4} - 8 q^{5} + 20 q^{6} + 8 q^{7} - 8 q^{8} + 35 q^{9} - 20 q^{10} + 50 q^{11} + 32 q^{12} - 22 q^{13} - 88 q^{14} - 304 q^{15} + 80 q^{16} - 62 q^{17} + 22 q^{18} + 19 q^{19} - 32 q^{20} - 48 q^{21} - 168 q^{22} - 154 q^{23} + 80 q^{24} + 229 q^{25} + 112 q^{26} + 368 q^{27} + 32 q^{28} - 226 q^{29} + 8 q^{30} + 228 q^{31} - 32 q^{32} + 28 q^{33} - 196 q^{34} + 906 q^{35} + 140 q^{36} + 346 q^{37} + 114 q^{38} + 42 q^{39} - 80 q^{40} - 1098 q^{41} - 812 q^{42} + 906 q^{43} + 200 q^{44} - 884 q^{45} + 600 q^{46} - 10 q^{47} + 128 q^{48} + 1705 q^{49} + 18 q^{50} - 1924 q^{51} - 88 q^{52} - 1254 q^{53} + 20 q^{54} - 850 q^{55} - 352 q^{56} + 114 q^{57} + 464 q^{58} - 416 q^{59} - 1216 q^{60} - 380 q^{61} + 392 q^{62} + 278 q^{63} + 320 q^{64} + 272 q^{65} - 216 q^{66} - 572 q^{67} - 248 q^{68} + 2020 q^{69} + 264 q^{70} + 1248 q^{71} + 88 q^{72} + 14 q^{73} + 76 q^{74} - 84 q^{75} + 76 q^{76} - 1298 q^{77} + 2120 q^{78} + 756 q^{79} - 128 q^{80} - 139 q^{81} + 1996 q^{82} + 1544 q^{83} - 192 q^{84} + 2358 q^{85} + 896 q^{86} + 2074 q^{87} - 672 q^{88} - 1706 q^{89} - 2588 q^{90} - 688 q^{91} - 616 q^{92} - 2140 q^{93} - 1536 q^{94} - 532 q^{95} + 320 q^{96} + 854 q^{97} - 3170 q^{98} - 826 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(38))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 19
38.4.a.a $1$ $2.242$ $$\Q$$ None $$-2$$ $$-2$$ $$-9$$ $$-31$$ $+$ $-$ $$q-2q^{2}-2q^{3}+4q^{4}-9q^{5}+4q^{6}+\cdots$$
38.4.a.b $2$ $2.242$ $$\Q(\sqrt{177})$$ None $$-4$$ $$1$$ $$10$$ $$57$$ $+$ $+$ $$q-2q^{2}+(1-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots$$
38.4.a.c $2$ $2.242$ $$\Q(\sqrt{73})$$ None $$4$$ $$9$$ $$-9$$ $$-18$$ $-$ $-$ $$q+2q^{2}+(5-\beta )q^{3}+4q^{4}+(-6+3\beta )q^{5}+\cdots$$

Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(38))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(38)) \simeq$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(19))$$$$^{\oplus 2}$$