Properties

Label 229.2.b
Level 229
Weight 2
Character orbit b
Rep. character \(\chi_{229}(228,\cdot)\)
Character field \(\Q\)
Dimension 18
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(229, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
229.2.b.a \(2\) \(1.829\) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(6\) \(0\) \(q+\beta q^{2}+q^{3}-3q^{4}+3q^{5}+\beta q^{6}+\cdots\)
229.2.b.b \(16\) \(1.829\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-12\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)