# Properties

 Label 14.2.a Level $14$ Weight $2$ Character orbit 14.a Rep. character $\chi_{14}(1,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $4$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$14 = 2 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 14.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$4$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(14))$$.

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

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

$$2$$$$7$$FrickeDim
$$+$$$$-$$$$-$$$$1$$
Plus space$$+$$$$0$$
Minus space$$-$$$$1$$

## Trace form

 $$q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10})$$ $$q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{12} - 4 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{18} + 2 q^{19} - 2 q^{21} + 2 q^{24} - 5 q^{25} + 4 q^{26} + 4 q^{27} + q^{28} - 6 q^{29} - 4 q^{31} - q^{32} - 6 q^{34} + q^{36} + 2 q^{37} - 2 q^{38} + 8 q^{39} + 6 q^{41} + 2 q^{42} + 8 q^{43} - 12 q^{47} - 2 q^{48} + q^{49} + 5 q^{50} - 12 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} - q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 8 q^{61} + 4 q^{62} + q^{63} + q^{64} - 4 q^{67} + 6 q^{68} - q^{72} + 2 q^{73} - 2 q^{74} + 10 q^{75} + 2 q^{76} - 8 q^{78} + 8 q^{79} - 11 q^{81} - 6 q^{82} - 6 q^{83} - 2 q^{84} - 8 q^{86} + 12 q^{87} - 6 q^{89} - 4 q^{91} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 10 q^{97} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(14))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
14.2.a.a $1$ $0.112$ $$\Q$$ None $$-1$$ $$-2$$ $$0$$ $$1$$ $+$ $-$ $$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$$