# Properties

 Label 381.2.a Level $381$ Weight $2$ Character orbit 381.a Rep. character $\chi_{381}(1,\cdot)$ Character field $\Q$ Dimension $21$ Newform subspaces $5$ Sturm bound $85$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$381 = 3 \cdot 127$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 381.a (trivial) Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$85$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(381))$$.

Total New Old
Modular forms 44 21 23
Cusp forms 41 21 20
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.

$$3$$$$127$$FrickeDim.
$$+$$$$+$$$$+$$$$5$$
$$+$$$$-$$$$-$$$$5$$
$$-$$$$+$$$$-$$$$10$$
$$-$$$$-$$$$+$$$$1$$
Plus space$$+$$$$6$$
Minus space$$-$$$$15$$

## Trace form

 $$21q + q^{2} + q^{3} + 21q^{4} - 6q^{5} - q^{6} + 4q^{7} - 3q^{8} + 21q^{9} + O(q^{10})$$ $$21q + q^{2} + q^{3} + 21q^{4} - 6q^{5} - q^{6} + 4q^{7} - 3q^{8} + 21q^{9} - 2q^{10} + 8q^{11} + 7q^{12} + 2q^{13} + 4q^{14} + 2q^{15} + 33q^{16} - 10q^{17} + q^{18} + 4q^{19} - 26q^{20} + 4q^{21} - 16q^{22} - 9q^{24} + 19q^{25} - 18q^{26} + q^{27} - 4q^{28} - 2q^{29} + 6q^{30} - 12q^{31} - 25q^{32} + 12q^{33} - 4q^{34} - 20q^{35} + 21q^{36} + 18q^{37} - 22q^{38} + 6q^{39} + 2q^{40} - 2q^{41} - 12q^{42} + 12q^{43} + 58q^{44} - 6q^{45} - 8q^{46} + 31q^{48} + 33q^{49} - 21q^{50} - 6q^{51} - 12q^{52} - 26q^{53} - q^{54} + 24q^{55} + 16q^{56} + 12q^{57} + 30q^{58} + 16q^{59} - 14q^{60} - 22q^{61} - 34q^{62} + 4q^{63} + 9q^{64} - 16q^{65} + 4q^{66} + 24q^{67} - 38q^{68} - 12q^{69} - 88q^{70} + 36q^{71} - 3q^{72} - 18q^{73} - 56q^{74} + 23q^{75} - 12q^{76} - 28q^{77} - 38q^{78} + 8q^{79} - 86q^{80} + 21q^{81} - 22q^{82} - 20q^{83} - 4q^{84} - 48q^{85} + 28q^{86} + 14q^{87} - 66q^{88} + 2q^{89} - 2q^{90} + 56q^{91} - 12q^{92} - 60q^{94} - 8q^{95} - 49q^{96} + 26q^{97} - 39q^{98} + 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(381))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 3 127
381.2.a.a $$1$$ $$3.042$$ $$\Q$$ None $$0$$ $$1$$ $$-1$$ $$-2$$ $$-$$ $$-$$ $$q+q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$$
381.2.a.b $$1$$ $$3.042$$ $$\Q$$ None $$2$$ $$1$$ $$3$$ $$-4$$ $$-$$ $$+$$ $$q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$$
381.2.a.c $$5$$ $$3.042$$ 5.5.81509.1 None $$-1$$ $$-5$$ $$-5$$ $$0$$ $$+$$ $$+$$ $$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$
381.2.a.d $$5$$ $$3.042$$ 5.5.246832.1 None $$2$$ $$-5$$ $$1$$ $$0$$ $$+$$ $$-$$ $$q+\beta _{2}q^{2}-q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots$$
381.2.a.e $$9$$ $$3.042$$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None $$-2$$ $$9$$ $$-4$$ $$10$$ $$-$$ $$+$$ $$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(381))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(381)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(127))$$$$^{\oplus 2}$$