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Properties

Label 157.2.a
Level $157$
Weight $2$
Character orbit 157.a
Rep. character $\chi_{157}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

\(157\)Dim
\(+\)\(5\)
\(-\)\(7\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(157))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 157
157.2.a.a 157.a 1.a $5$ $1.254$ 5.5.24217.1 None \(-5\) \(-7\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
157.2.a.b 157.a 1.a $7$ $1.254$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(5\) \(5\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{4})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)