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Properties

Label 229.2.b
Level $229$
Weight $2$
Character orbit 229.b
Rep. character $\chi_{229}(228,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $2$
Sturm bound $38$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 229.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 229 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(38\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(229, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 18 18 0
Eisenstein series 2 2 0

Trace form

\( 18 q + 2 q^{3} - 22 q^{4} - 6 q^{5} + 16 q^{9} + O(q^{10}) \) \( 18 q + 2 q^{3} - 22 q^{4} - 6 q^{5} + 16 q^{9} - 2 q^{11} - 18 q^{12} + 2 q^{14} - 14 q^{15} + 10 q^{16} + 8 q^{17} - 4 q^{19} + 26 q^{20} - 2 q^{26} + 20 q^{27} - 20 q^{33} - 58 q^{36} - 30 q^{37} - 58 q^{42} + 36 q^{43} + 32 q^{44} - 40 q^{45} + 56 q^{46} + 74 q^{48} - 30 q^{49} + 10 q^{51} - 16 q^{53} + 26 q^{56} + 36 q^{57} - 34 q^{58} + 28 q^{60} + 36 q^{61} + 4 q^{62} - 42 q^{64} - 76 q^{68} + 28 q^{70} - 18 q^{71} - 16 q^{75} + 80 q^{76} + 22 q^{78} - 36 q^{80} + 18 q^{81} + 52 q^{82} - 10 q^{83} - 42 q^{85} + 24 q^{91} + 34 q^{94} - 2 q^{95} - 44 q^{97} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(229, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
229.2.b.a 229.b 229.b $2$ $1.829$ \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+q^{3}-3q^{4}+3q^{5}+\beta q^{6}+\cdots\)
229.2.b.b 229.b 229.b $16$ $1.829$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)