# Properties

 Label 157.2.a Level 157 Weight 2 Character orbit a Rep. character $$\chi_{157}(1,\cdot)$$ Character field $$\Q$$ Dimension 12 Newforms 2 Sturm bound 26 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$157$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 157.a (trivial) Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$26$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(157))$$.

Total New Old
Modular forms 13 13 0
Cusp forms 12 12 0
Eisenstein series 1 1 0

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

$$157$$Dim.
$$+$$$$5$$
$$-$$$$7$$

## Trace form

 $$12q - 2q^{3} + 12q^{4} - 4q^{5} + 6q^{6} - 2q^{7} + 10q^{9} + O(q^{10})$$ $$12q - 2q^{3} + 12q^{4} - 4q^{5} + 6q^{6} - 2q^{7} + 10q^{9} - 10q^{10} - 4q^{11} - 16q^{12} - 12q^{13} - 10q^{14} - 10q^{15} + 16q^{16} - 4q^{17} - 18q^{18} - 6q^{19} - 18q^{20} + 18q^{22} + 2q^{23} + 16q^{24} + 6q^{25} + 18q^{26} + 10q^{27} - 8q^{28} + 6q^{29} - 10q^{31} + 10q^{32} + 22q^{33} - 4q^{34} - 2q^{35} + 16q^{36} - 12q^{37} - 4q^{38} - 8q^{39} - 10q^{40} + 8q^{41} - 12q^{43} - 8q^{44} + 2q^{45} + 38q^{46} - 50q^{48} - 12q^{49} + 22q^{50} - 24q^{52} - 16q^{53} + 36q^{54} - 16q^{55} - 42q^{56} + 16q^{57} + 28q^{58} + 38q^{59} - 30q^{60} - 2q^{61} - 22q^{62} + 14q^{63} + 62q^{64} - 16q^{66} - 8q^{67} + 6q^{68} + 18q^{69} + 50q^{70} - 4q^{71} - 100q^{72} - 6q^{73} - 22q^{74} + 28q^{75} - 22q^{76} + 8q^{77} - 4q^{78} + 28q^{79} - 64q^{80} + 20q^{81} - 20q^{82} + 14q^{83} - 64q^{84} - 16q^{85} + 62q^{86} + 14q^{87} + 36q^{88} + 12q^{89} - 38q^{90} - 26q^{91} + 16q^{92} - 24q^{93} + 22q^{94} + 36q^{95} + 82q^{96} + 8q^{97} + 36q^{98} + 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(157))$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 157
157.2.a.a $$5$$ $$1.254$$ 5.5.24217.1 None $$-5$$ $$-7$$ $$-3$$ $$-3$$ $$+$$ $$q+(-1+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$$
157.2.a.b $$7$$ $$1.254$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$5$$ $$5$$ $$-1$$ $$1$$ $$-$$ $$q+(1-\beta _{1})q^{2}+(1+\beta _{4})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$$