Properties

Label 552.2.bf
Level $552$
Weight $2$
Character orbit 552.bf
Rep. character $\chi_{552}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $920$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.bf (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 552 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(552, [\chi])\).

Total New Old
Modular forms 1000 1000 0
Cusp forms 920 920 0
Eisenstein series 80 80 0

Trace form

\( 920q - 22q^{4} - 2q^{6} - 44q^{7} - 18q^{9} + O(q^{10}) \) \( 920q - 22q^{4} - 2q^{6} - 44q^{7} - 18q^{9} - 22q^{10} - 12q^{12} - 22q^{15} - 30q^{16} - 10q^{18} - 14q^{24} + 40q^{25} - 22q^{28} - 11q^{30} - 20q^{31} - 22q^{33} - 18q^{36} - 42q^{39} - 176q^{40} - 11q^{42} + 90q^{46} - 64q^{48} + 32q^{49} - 90q^{52} + 21q^{54} - 76q^{55} - 22q^{57} + 76q^{58} - 11q^{60} - 22q^{63} - 28q^{64} - 44q^{66} - 116q^{70} - 79q^{72} - 36q^{73} - 22q^{76} - 134q^{78} - 44q^{79} - 34q^{81} - 40q^{82} - 165q^{84} - 18q^{87} - 22q^{88} - 198q^{90} + 88q^{94} - 231q^{96} - 44q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(552, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
552.2.bf.a \(920\) \(4.408\) None \(0\) \(0\) \(0\) \(-44\)