# Properties

 Label 44.2.a Level $44$ Weight $2$ Character orbit 44.a Rep. character $\chi_{44}(1,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$44 = 2^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 44.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 $$M_{2}(\Gamma_0(44))$$.

Total New Old
Modular forms 9 1 8
Cusp forms 4 1 3
Eisenstein series 5 0 5

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

$$2$$$$11$$FrickeDim
$$-$$$$+$$$-$$$1$$
Plus space$$+$$$$0$$
Minus space$$-$$$$1$$

## Trace form

 $$q + q^{3} - 3 q^{5} + 2 q^{7} - 2 q^{9} + O(q^{10})$$ $$q + q^{3} - 3 q^{5} + 2 q^{7} - 2 q^{9} - q^{11} - 4 q^{13} - 3 q^{15} + 6 q^{17} + 8 q^{19} + 2 q^{21} - 3 q^{23} + 4 q^{25} - 5 q^{27} + 5 q^{31} - q^{33} - 6 q^{35} - q^{37} - 4 q^{39} - 10 q^{43} + 6 q^{45} - 3 q^{49} + 6 q^{51} - 6 q^{53} + 3 q^{55} + 8 q^{57} + 3 q^{59} - 4 q^{61} - 4 q^{63} + 12 q^{65} - q^{67} - 3 q^{69} + 15 q^{71} - 4 q^{73} + 4 q^{75} - 2 q^{77} + 2 q^{79} + q^{81} + 6 q^{83} - 18 q^{85} - 9 q^{89} - 8 q^{91} + 5 q^{93} - 24 q^{95} - 7 q^{97} + 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(44))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11
44.2.a.a $1$ $0.351$ $$\Q$$ None $$0$$ $$1$$ $$-3$$ $$2$$ $-$ $+$ $$q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(44))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(44)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(11))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(22))$$$$^{\oplus 2}$$