# Properties

 Label 1444.2.a Level $1444$ Weight $2$ Character orbit 1444.a Rep. character $\chi_{1444}(1,\cdot)$ Character field $\Q$ Dimension $29$ Newform subspaces $9$ Sturm bound $380$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1444 = 2^{2} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1444.a (trivial) Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$380$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(1444))$$.

Total New Old
Modular forms 220 29 191
Cusp forms 161 29 132
Eisenstein series 59 0 59

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
$$-$$$$+$$$$-$$$$17$$
$$-$$$$-$$$$+$$$$12$$
Plus space$$+$$$$12$$
Minus space$$-$$$$17$$

## Trace form

 $$29 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 29 q^{9} + O(q^{10})$$ $$29 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 29 q^{9} - 4 q^{11} + 4 q^{13} + 2 q^{15} + 4 q^{17} + 6 q^{21} - 10 q^{23} + 35 q^{25} + 4 q^{27} + 2 q^{29} - 4 q^{31} - 10 q^{33} - 4 q^{35} - 10 q^{37} + 2 q^{39} - 10 q^{41} + 4 q^{43} + 6 q^{45} - 4 q^{47} + 33 q^{49} + 6 q^{51} + 4 q^{53} + 8 q^{55} - 6 q^{59} + 10 q^{61} + 2 q^{63} - 4 q^{65} + 12 q^{67} - 16 q^{69} - 2 q^{71} - 8 q^{73} + 8 q^{75} + 14 q^{77} - 8 q^{79} + 45 q^{81} + 14 q^{83} + 2 q^{87} - 12 q^{89} - 12 q^{91} - 8 q^{93} + 8 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(1444))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 19
1444.2.a.a $1$ $11.530$ $$\Q$$ None $$0$$ $$-2$$ $$-1$$ $$-3$$ $-$ $-$ $$q-2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots$$
1444.2.a.b $1$ $11.530$ $$\Q$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $-$ $+$ $$q-q^{3}-q^{5}-2q^{9}-4q^{11}-q^{13}+\cdots$$
1444.2.a.c $1$ $11.530$ $$\Q$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $-$ $-$ $$q+q^{3}-q^{5}-2q^{9}-4q^{11}+q^{13}+\cdots$$
1444.2.a.d $2$ $11.530$ $$\Q(\sqrt{5})$$ None $$0$$ $$-1$$ $$-2$$ $$4$$ $-$ $-$ $$q-\beta q^{3}-2\beta q^{5}+(1+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$$
1444.2.a.e $2$ $11.530$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$1$$ $$-3$$ $-$ $+$ $$q+\beta q^{5}+(-2+\beta )q^{7}-3q^{9}+(2+\beta )q^{11}+\cdots$$
1444.2.a.f $2$ $11.530$ $$\Q(\sqrt{5})$$ None $$0$$ $$1$$ $$-2$$ $$4$$ $-$ $-$ $$q+\beta q^{3}-2\beta q^{5}+(1+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$$
1444.2.a.g $6$ $11.530$ 6.6.20319417.1 None $$0$$ $$-3$$ $$-3$$ $$-3$$ $-$ $-$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots$$
1444.2.a.h $6$ $11.530$ 6.6.20319417.1 None $$0$$ $$3$$ $$-3$$ $$-3$$ $-$ $+$ $$q+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots$$
1444.2.a.i $8$ $11.530$ 8.8.$$\cdots$$.1 None $$0$$ $$0$$ $$14$$ $$8$$ $-$ $+$ $$q+(\beta _{3}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(1444))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(1444)) \simeq$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(361))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(722))$$$$^{\oplus 2}$$