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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

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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

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

Display 100 coefficients 10 coefficients

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 \(5\) \(5\) \(-1\) \(1\) \(-\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{4})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)