# Properties

 Label 153.4.a Level $153$ Weight $4$ Character orbit 153.a Rep. character $\chi_{153}(1,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $9$ Sturm bound $72$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$153 = 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 153.a (trivial) Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$72$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(153))$$.

Total New Old
Modular forms 58 20 38
Cusp forms 50 20 30
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.

$$3$$$$17$$FrickeDim.
$$+$$$$+$$$$+$$$$4$$
$$+$$$$-$$$$-$$$$4$$
$$-$$$$+$$$$-$$$$5$$
$$-$$$$-$$$$+$$$$7$$
Plus space$$+$$$$11$$
Minus space$$-$$$$9$$

## Trace form

 $$20 q - 2 q^{2} + 90 q^{4} + 2 q^{5} - 46 q^{7} - 30 q^{8} + O(q^{10})$$ $$20 q - 2 q^{2} + 90 q^{4} + 2 q^{5} - 46 q^{7} - 30 q^{8} + 22 q^{10} + 36 q^{11} + 76 q^{13} + 112 q^{14} + 298 q^{16} + 34 q^{17} + 60 q^{19} + 130 q^{20} - 434 q^{22} - 82 q^{23} + 496 q^{25} + 4 q^{26} - 168 q^{28} - 6 q^{29} - 702 q^{31} + 338 q^{32} - 68 q^{34} + 20 q^{35} - 318 q^{37} + 380 q^{38} + 542 q^{40} - 804 q^{41} + 848 q^{43} + 90 q^{44} - 284 q^{46} - 1032 q^{47} + 220 q^{49} - 862 q^{50} - 1784 q^{52} + 12 q^{53} - 908 q^{55} + 960 q^{56} + 1654 q^{58} - 816 q^{59} - 1982 q^{61} - 776 q^{62} + 3730 q^{64} + 596 q^{65} + 460 q^{67} + 408 q^{68} - 736 q^{70} + 3238 q^{71} - 2272 q^{73} - 914 q^{74} + 3344 q^{76} + 1104 q^{77} + 1666 q^{79} + 2434 q^{80} - 1568 q^{82} - 872 q^{83} - 578 q^{85} + 40 q^{86} - 6586 q^{88} + 1064 q^{89} + 1440 q^{91} - 4484 q^{92} - 696 q^{94} + 2800 q^{95} + 2356 q^{97} - 6042 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(153))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 17
153.4.a.a $1$ $9.027$ $$\Q$$ None $$-1$$ $$0$$ $$10$$ $$-8$$ $-$ $+$ $$q-q^{2}-7q^{4}+10q^{5}-8q^{7}+15q^{8}+\cdots$$
153.4.a.b $1$ $9.027$ $$\Q$$ None $$1$$ $$0$$ $$-16$$ $$34$$ $-$ $-$ $$q+q^{2}-7q^{4}-2^{4}q^{5}+34q^{7}-15q^{8}+\cdots$$
153.4.a.c $1$ $9.027$ $$\Q$$ None $$1$$ $$0$$ $$20$$ $$-2$$ $-$ $-$ $$q+q^{2}-7q^{4}+20q^{5}-2q^{7}-15q^{8}+\cdots$$
153.4.a.d $1$ $9.027$ $$\Q$$ None $$3$$ $$0$$ $$-6$$ $$-28$$ $-$ $+$ $$q+3q^{2}+q^{4}-6q^{5}-28q^{7}-21q^{8}+\cdots$$
153.4.a.e $2$ $9.027$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$-6$$ $$-8$$ $-$ $-$ $$q+\beta q^{2}+10q^{4}+(-3+4\beta )q^{5}+(-4+\cdots)q^{7}+\cdots$$
153.4.a.f $3$ $9.027$ 3.3.5912.1 None $$-5$$ $$0$$ $$-8$$ $$-8$$ $-$ $+$ $$q+(-2+\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots$$
153.4.a.g $3$ $9.027$ 3.3.2636.1 None $$-1$$ $$0$$ $$8$$ $$22$$ $-$ $-$ $$q+(-\beta _{1}+\beta _{2})q^{2}+(8-3\beta _{1}-\beta _{2})q^{4}+\cdots$$
153.4.a.h $4$ $9.027$ 4.4.1506848.1 None $$-4$$ $$0$$ $$-22$$ $$-24$$ $+$ $-$ $$q+(-1-\beta _{2})q^{2}+(6+2\beta _{2}-\beta _{3})q^{4}+\cdots$$
153.4.a.i $4$ $9.027$ 4.4.1506848.1 None $$4$$ $$0$$ $$22$$ $$-24$$ $+$ $+$ $$q+(1-\beta _{2})q^{2}+(6-2\beta _{2}-\beta _{3})q^{4}+(5+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(153))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(153)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(17))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(51))$$$$^{\oplus 2}$$