# Properties

 Label 592.2.a Level $592$ Weight $2$ Character orbit 592.a Rep. character $\chi_{592}(1,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $10$ Sturm bound $152$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$592 = 2^{4} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 592.a (trivial) Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$152$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(592))$$.

Total New Old
Modular forms 82 18 64
Cusp forms 71 18 53
Eisenstein series 11 0 11

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

$$2$$$$37$$FrickeDim
$$+$$$$+$$$$+$$$$4$$
$$+$$$$-$$$$-$$$$5$$
$$-$$$$+$$$$-$$$$5$$
$$-$$$$-$$$$+$$$$4$$
Plus space$$+$$$$8$$
Minus space$$-$$$$10$$

## Trace form

 $$18 q + 14 q^{9} + O(q^{10})$$ $$18 q + 14 q^{9} - 4 q^{15} - 4 q^{17} - 2 q^{19} - 8 q^{21} + 6 q^{23} + 10 q^{25} - 12 q^{27} - 8 q^{29} - 14 q^{31} - 8 q^{33} + 12 q^{35} + 4 q^{39} + 4 q^{41} - 10 q^{43} - 8 q^{45} + 10 q^{49} + 28 q^{51} - 8 q^{53} + 12 q^{55} - 16 q^{57} + 2 q^{59} + 8 q^{61} + 36 q^{63} - 16 q^{65} + 12 q^{67} - 8 q^{69} + 8 q^{71} - 20 q^{73} + 20 q^{75} - 24 q^{77} - 6 q^{79} + 2 q^{81} - 8 q^{83} + 16 q^{85} - 4 q^{89} - 28 q^{91} + 8 q^{93} + 28 q^{95} - 12 q^{97} + 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(592))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
592.2.a.a $1$ $4.727$ $$\Q$$ None $$0$$ $$-1$$ $$0$$ $$1$$ $-$ $-$ $$q-q^{3}+q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots$$
592.2.a.b $1$ $4.727$ $$\Q$$ None $$0$$ $$1$$ $$-4$$ $$3$$ $-$ $-$ $$q+q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots$$
592.2.a.c $1$ $4.727$ $$\Q$$ None $$0$$ $$1$$ $$-2$$ $$-1$$ $+$ $+$ $$q+q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots$$
592.2.a.d $1$ $4.727$ $$\Q$$ None $$0$$ $$1$$ $$0$$ $$3$$ $+$ $-$ $$q+q^{3}+3q^{7}-2q^{9}+3q^{11}+2q^{17}+\cdots$$
592.2.a.e $1$ $4.727$ $$\Q$$ None $$0$$ $$3$$ $$-2$$ $$1$$ $-$ $+$ $$q+3q^{3}-2q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots$$
592.2.a.f $2$ $4.727$ $$\Q(\sqrt{13})$$ None $$0$$ $$-3$$ $$-1$$ $$-2$$ $-$ $-$ $$q+(-1-\beta )q^{3}-\beta q^{5}+(-2+2\beta )q^{7}+\cdots$$
592.2.a.g $2$ $4.727$ $$\Q(\sqrt{5})$$ None $$0$$ $$1$$ $$1$$ $$2$$ $-$ $+$ $$q+\beta q^{3}+(-1+3\beta )q^{5}+2\beta q^{7}+(-2+\cdots)q^{9}+\cdots$$
592.2.a.h $2$ $4.727$ $$\Q(\sqrt{17})$$ None $$0$$ $$1$$ $$4$$ $$-1$$ $-$ $+$ $$q+\beta q^{3}+2q^{5}-\beta q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots$$
592.2.a.i $3$ $4.727$ 3.3.229.1 None $$0$$ $$-2$$ $$-1$$ $$-7$$ $+$ $+$ $$q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$$
592.2.a.j $4$ $4.727$ 4.4.48389.1 None $$0$$ $$-2$$ $$5$$ $$1$$ $+$ $-$ $$q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(592))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(592)) \simeq$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(37))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(74))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(148))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(296))$$$$^{\oplus 2}$$