Properties

Label 552.2.x
Level $552$
Weight $2$
Character orbit 552.x
Rep. character $\chi_{552}(35,\cdot)$
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.x (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

\( 920q - 18q^{3} - 14q^{4} - 16q^{6} - 18q^{9} + O(q^{10}) \) \( 920q - 18q^{3} - 14q^{4} - 16q^{6} - 18q^{9} - 14q^{10} - 6q^{12} - 30q^{16} - 16q^{18} - 52q^{19} - 32q^{22} - 26q^{24} - 112q^{25} - 30q^{27} - 34q^{28} + 11q^{30} - 30q^{33} - 88q^{34} - 18q^{36} + 124q^{40} - 3q^{42} - 36q^{43} - 110q^{46} + 32q^{49} - 30q^{51} + 90q^{52} - 39q^{54} - 6q^{57} - 68q^{58} + 13q^{60} + 28q^{64} - 46q^{66} - 100q^{67} - 92q^{70} + 29q^{72} - 36q^{73} + 14q^{75} - 50q^{76} - 86q^{78} - 2q^{81} - 12q^{82} - 151q^{84} - 42q^{88} - 196q^{90} - 136q^{91} - 68q^{94} - 175q^{96} - 36q^{97} - 54q^{99} + O(q^{100}) \)

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.x.a \(920\) \(4.408\) None \(0\) \(-18\) \(0\) \(0\)