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Properties

Label 431.2.a
Level $431$
Weight $2$
Character orbit 431.a
Rep. character $\chi_{431}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $6$
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: \(\Q\)
Newform subspaces: \( 6 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(431))\) into newform subspaces

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