Properties

Label 431.2.a
Level 431
Weight 2
Character orbit a
Rep. character \(\chi_{431}(1,\cdot)\)
Character field \(\Q\)
Dimension 36
Newforms 6
Sturm bound 72
Trace bound 3

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Defining parameters

Level: \( N \) = \( 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 431.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(431))\).

Total New Old
Modular forms 37 37 0
Cusp forms 36 36 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.

\(431\)Dim.
\(+\)\(8\)
\(-\)\(28\)

Trace form

\( 36q - q^{2} + 2q^{3} + 37q^{4} + 4q^{5} + 6q^{6} + 4q^{7} - 3q^{8} + 40q^{9} + O(q^{10}) \) \( 36q - q^{2} + 2q^{3} + 37q^{4} + 4q^{5} + 6q^{6} + 4q^{7} - 3q^{8} + 40q^{9} - 2q^{10} - 2q^{12} + 4q^{13} - 8q^{14} + 35q^{16} + 4q^{17} - 23q^{18} + 12q^{19} - 2q^{20} + 2q^{21} - 12q^{22} + 16q^{24} + 48q^{25} + 2q^{26} + 8q^{27} - 4q^{28} + 4q^{29} - 16q^{30} + 22q^{31} - 17q^{32} + 6q^{33} + 18q^{34} - 14q^{35} + 55q^{36} + 16q^{37} - 22q^{38} - 12q^{39} + 4q^{40} + 20q^{41} - 4q^{42} - 2q^{43} - 10q^{44} + 42q^{45} + 12q^{46} + 4q^{47} - 42q^{48} + 68q^{49} - 13q^{50} - 34q^{51} + 18q^{52} - 10q^{53} + 10q^{54} + 2q^{55} - 58q^{56} + 18q^{57} + 24q^{58} + 18q^{59} - 52q^{60} + 28q^{61} - 40q^{62} - 10q^{63} + 17q^{64} + 12q^{65} - 30q^{66} - 12q^{67} - 8q^{68} + 4q^{69} - 40q^{70} - 8q^{71} - 89q^{72} + 52q^{73} - 64q^{74} - 18q^{75} + 18q^{76} - 10q^{77} - 84q^{78} - 4q^{79} - 28q^{80} + 20q^{81} + 24q^{82} - 48q^{83} - 100q^{84} + 18q^{85} + 14q^{86} - 40q^{87} - 80q^{88} + 26q^{89} - 154q^{90} + 48q^{91} - 80q^{92} - 24q^{93} + 28q^{94} - 36q^{95} + 54q^{97} - 123q^{98} - 14q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(431))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 431
431.2.a.a \(1\) \(3.442\) \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
431.2.a.b \(1\) \(3.442\) \(\Q\) None \(-1\) \(3\) \(-3\) \(2\) \(-\) \(q-q^{2}+3q^{3}-q^{4}-3q^{5}-3q^{6}+2q^{7}+\cdots\)
431.2.a.c \(3\) \(3.442\) 3.3.473.1 None \(0\) \(1\) \(1\) \(0\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
431.2.a.d \(3\) \(3.442\) 3.3.257.1 None \(1\) \(-1\) \(-3\) \(-6\) \(+\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
431.2.a.e \(4\) \(3.442\) 4.4.725.1 None \(-1\) \(-3\) \(-5\) \(2\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
431.2.a.f \(24\) \(3.442\) None \(1\) \(1\) \(13\) \(8\) \(-\)