# Properties

 Label 671.2.a Level 671 Weight 2 Character orbit a Rep. character $$\chi_{671}(1,\cdot)$$ Character field $$\Q$$ Dimension 51 Newform subspaces 4 Sturm bound 124 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$671 = 11 \cdot 61$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 671.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$124$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(671))$$.

Total New Old
Modular forms 64 51 13
Cusp forms 61 51 10
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.

$$11$$$$61$$FrickeDim.
$$+$$$$+$$$$+$$$$6$$
$$+$$$$-$$$$-$$$$21$$
$$-$$$$+$$$$-$$$$19$$
$$-$$$$-$$$$+$$$$5$$
Plus space$$+$$$$11$$
Minus space$$-$$$$40$$

## Trace form

 $$51q + 3q^{2} + 2q^{3} + 57q^{4} + 4q^{5} + 8q^{7} - 9q^{8} + 61q^{9} + O(q^{10})$$ $$51q + 3q^{2} + 2q^{3} + 57q^{4} + 4q^{5} + 8q^{7} - 9q^{8} + 61q^{9} + 6q^{10} - 3q^{11} + 8q^{12} + 14q^{13} + 4q^{14} + 2q^{15} + 73q^{16} + 2q^{17} - q^{18} + 16q^{19} - 14q^{20} + 20q^{21} + 3q^{22} - 2q^{23} + 8q^{24} + 67q^{25} + 10q^{26} - 34q^{27} + 12q^{28} + 10q^{29} - 12q^{30} + 6q^{31} + 15q^{32} - 2q^{33} + 6q^{34} - 28q^{35} + 101q^{36} + 16q^{37} - 20q^{38} - 8q^{39} - 6q^{40} + 10q^{41} - 20q^{42} + 36q^{43} - 11q^{44} + 22q^{45} + 24q^{46} - 12q^{47} - 64q^{48} + 91q^{49} + 29q^{50} + 32q^{51} + 22q^{52} + 6q^{53} - 16q^{54} - 8q^{55} + 24q^{56} + 44q^{57} - 14q^{58} - 34q^{59} - 28q^{60} + q^{61} + 4q^{63} + 113q^{64} + 48q^{65} - 8q^{66} + 22q^{67} - 18q^{68} - 34q^{69} - 28q^{70} - 18q^{71} - 37q^{72} + 22q^{73} - 26q^{74} - 52q^{75} + 4q^{76} + 8q^{77} - 112q^{78} + 48q^{79} - 50q^{80} + 123q^{81} - 42q^{82} - 4q^{83} - 60q^{84} + 56q^{85} - 32q^{86} - 36q^{87} + 15q^{88} - 126q^{90} + 48q^{91} + 12q^{92} - 42q^{93} + 12q^{94} - 36q^{95} - 44q^{96} + 60q^{97} - 77q^{98} - 9q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(671))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 11 61
671.2.a.a $$5$$ $$5.358$$ 5.5.24217.1 None $$-2$$ $$0$$ $$-2$$ $$-1$$ $$-$$ $$-$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$$
671.2.a.b $$6$$ $$5.358$$ 6.6.2661761.1 None $$0$$ $$-1$$ $$-1$$ $$-5$$ $$+$$ $$+$$ $$q+\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
671.2.a.c $$19$$ $$5.358$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None $$5$$ $$0$$ $$0$$ $$9$$ $$-$$ $$+$$ $$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$$
671.2.a.d $$21$$ $$5.358$$ None $$0$$ $$3$$ $$7$$ $$5$$ $$+$$ $$-$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(671))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(671)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(11))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(61))$$$$^{\oplus 2}$$