Properties

Label 229.2.a
Level 229
Weight 2
Character orbit a
Rep. character \(\chi_{229}(1,\cdot)\)
Character field \(\Q\)
Dimension 18
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(229))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 229
229.2.a.a \(1\) \(1.829\) \(\Q\) None \(-1\) \(1\) \(-3\) \(2\) \(+\) \(q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}+2q^{7}+\cdots\)
229.2.a.b \(6\) \(1.829\) 6.6.1868969.1 None \(-4\) \(-6\) \(-3\) \(-5\) \(+\) \(q+(-1-\beta _{5})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
229.2.a.c \(11\) \(1.829\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(5\) \(3\) \(0\) \(1\) \(-\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)