Properties

 Label 18.4.a Level $18$ Weight $4$ Character orbit 18.a Rep. character $\chi_{18}(1,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 18.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(18))$$.

Total New Old
Modular forms 13 1 12
Cusp forms 5 1 4
Eisenstein series 8 0 8

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

$$2$$$$3$$FrickeDim.
$$-$$$$-$$$$+$$$$1$$
Plus space$$+$$$$1$$
Minus space$$-$$$$0$$

Trace form

 $$q + 2 q^{2} + 4 q^{4} - 6 q^{5} - 16 q^{7} + 8 q^{8} + O(q^{10})$$ $$q + 2 q^{2} + 4 q^{4} - 6 q^{5} - 16 q^{7} + 8 q^{8} - 12 q^{10} - 12 q^{11} + 38 q^{13} - 32 q^{14} + 16 q^{16} + 126 q^{17} + 20 q^{19} - 24 q^{20} - 24 q^{22} - 168 q^{23} - 89 q^{25} + 76 q^{26} - 64 q^{28} - 30 q^{29} - 88 q^{31} + 32 q^{32} + 252 q^{34} + 96 q^{35} + 254 q^{37} + 40 q^{38} - 48 q^{40} - 42 q^{41} - 52 q^{43} - 48 q^{44} - 336 q^{46} + 96 q^{47} - 87 q^{49} - 178 q^{50} + 152 q^{52} - 198 q^{53} + 72 q^{55} - 128 q^{56} - 60 q^{58} + 660 q^{59} - 538 q^{61} - 176 q^{62} + 64 q^{64} - 228 q^{65} + 884 q^{67} + 504 q^{68} + 192 q^{70} - 792 q^{71} + 218 q^{73} + 508 q^{74} + 80 q^{76} + 192 q^{77} - 520 q^{79} - 96 q^{80} - 84 q^{82} + 492 q^{83} - 756 q^{85} - 104 q^{86} - 96 q^{88} - 810 q^{89} - 608 q^{91} - 672 q^{92} + 192 q^{94} - 120 q^{95} + 1154 q^{97} - 174 q^{98} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(18))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
18.4.a.a $1$ $1.062$ $$\Q$$ None $$2$$ $$0$$ $$-6$$ $$-16$$ $-$ $-$ $$q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots$$

Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(18))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(18)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(6))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(9))$$$$^{\oplus 2}$$