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Properties

Label 229.2.a
Level $229$
Weight $2$
Character orbit 229.a
Rep. character $\chi_{229}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $3$
Sturm bound $38$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 229.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(38\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(229))\).

Total New Old
Modular forms 19 19 0
Cusp forms 18 18 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.

\(229\)Dim
\(+\)\(7\)
\(-\)\(11\)

Trace form

\( 18 q - 2 q^{3} + 14 q^{4} - 6 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} + 16 q^{9} + O(q^{10}) \) \( 18 q - 2 q^{3} + 14 q^{4} - 6 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} + 16 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 12 q^{13} + 2 q^{14} - 10 q^{15} + 10 q^{16} - 8 q^{18} - 8 q^{19} - 26 q^{20} - 18 q^{21} + 30 q^{22} - 8 q^{23} - 14 q^{24} + 8 q^{25} - 18 q^{26} - 8 q^{27} - 12 q^{28} + 4 q^{29} - 20 q^{30} - 2 q^{31} + 32 q^{32} + 16 q^{33} - 14 q^{34} + 10 q^{35} + 14 q^{36} - 10 q^{37} + 12 q^{38} + 28 q^{39} - 26 q^{40} + 12 q^{41} - 2 q^{42} - 4 q^{43} - 16 q^{44} - 16 q^{45} - 28 q^{46} + 16 q^{47} - 10 q^{48} + 2 q^{49} + 32 q^{50} + 14 q^{51} - 26 q^{52} - 16 q^{53} - 14 q^{54} + 6 q^{56} + 4 q^{57} - 2 q^{58} + 24 q^{59} - 16 q^{60} - 24 q^{61} + 8 q^{62} + 12 q^{63} + 22 q^{64} + 4 q^{66} + 10 q^{67} + 20 q^{68} - 22 q^{69} - 4 q^{70} - 10 q^{71} + 6 q^{72} - 2 q^{73} - 10 q^{74} + 8 q^{75} - 12 q^{76} - 10 q^{77} + 30 q^{78} + 2 q^{79} - 64 q^{80} - 14 q^{81} + 36 q^{82} + 34 q^{83} - 102 q^{84} - 10 q^{85} + 74 q^{86} - 14 q^{87} + 112 q^{88} - 18 q^{89} + 42 q^{90} - 4 q^{91} - 30 q^{92} + 6 q^{93} + 14 q^{94} + 6 q^{95} - 68 q^{96} - 58 q^{98} + 22 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(229))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 229
229.2.a.a 229.a 1.a $1$ $1.829$ \(\Q\) None \(-1\) \(1\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}+2q^{7}+\cdots\)
229.2.a.b 229.a 1.a $6$ $1.829$ 6.6.1868969.1 None \(-4\) \(-6\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{5})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
229.2.a.c 229.a 1.a $11$ $1.829$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(5\) \(3\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)