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Properties

Label 151.2.a
Level $151$
Weight $2$
Character orbit 151.a
Rep. character $\chi_{151}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
Sturm bound $25$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 151.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(25\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(151))\).

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.

\(151\)Dim
\(+\)\(3\)
\(-\)\(9\)

Trace form

\( 12 q - q^{2} + 7 q^{4} + 4 q^{5} - 6 q^{6} - 6 q^{7} - 3 q^{8} + 14 q^{9} + O(q^{10}) \) \( 12 q - q^{2} + 7 q^{4} + 4 q^{5} - 6 q^{6} - 6 q^{7} - 3 q^{8} + 14 q^{9} + 4 q^{10} + 2 q^{11} + 4 q^{12} - 4 q^{13} + 8 q^{14} - 8 q^{15} + q^{16} + 10 q^{17} - 11 q^{18} - 6 q^{19} + 4 q^{20} + 2 q^{21} - 12 q^{22} - 4 q^{23} - 16 q^{24} + 16 q^{25} + 14 q^{26} - 12 q^{27} - 32 q^{28} - 24 q^{30} - 10 q^{31} - 7 q^{32} - 2 q^{33} - 16 q^{34} + 2 q^{35} - 21 q^{36} + 4 q^{37} + 9 q^{38} - 28 q^{39} - 3 q^{40} + 20 q^{41} - 20 q^{42} + 16 q^{43} + 23 q^{44} + 24 q^{45} + 10 q^{46} + 18 q^{47} + 10 q^{48} + 6 q^{49} - 24 q^{50} - 8 q^{51} - 14 q^{52} + 42 q^{54} - 2 q^{55} + 12 q^{56} - 28 q^{57} - q^{58} + 34 q^{59} + 12 q^{60} - 4 q^{61} - 4 q^{62} + 2 q^{63} - 45 q^{64} - 6 q^{66} - 14 q^{67} + 25 q^{68} + 26 q^{69} - 18 q^{70} - 16 q^{71} - 11 q^{72} + 2 q^{73} + 12 q^{74} + 8 q^{75} - 4 q^{76} - 8 q^{77} + 44 q^{78} - 38 q^{79} + 51 q^{80} + 28 q^{81} + 38 q^{82} + 14 q^{83} + 26 q^{84} + 44 q^{85} - 30 q^{86} + 6 q^{87} + 10 q^{88} + 36 q^{89} - 6 q^{90} - 30 q^{91} - 56 q^{92} + 2 q^{93} + 11 q^{94} + 36 q^{95} - 40 q^{96} + 6 q^{97} + 27 q^{98} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(151))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 151
151.2.a.a 151.a 1.a $3$ $1.206$ \(\Q(\zeta_{14})^+\) None \(-2\) \(-1\) \(-7\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
151.2.a.b 151.a 1.a $3$ $1.206$ 3.3.257.1 None \(0\) \(6\) \(5\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+2q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
151.2.a.c 151.a 1.a $6$ $1.206$ 6.6.4838537.1 None \(1\) \(-5\) \(6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)