Properties

Label 552.2.b
Level $552$
Weight $2$
Character orbit 552.b
Rep. character $\chi_{552}(413,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $3$
Sturm bound $192$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 552 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(29\)

Dimensions

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

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

Trace form

\( 92q - 9q^{6} - 4q^{9} + O(q^{10}) \) \( 92q - 9q^{6} - 4q^{9} + q^{12} + 8q^{16} - q^{18} - 8q^{24} - 84q^{25} - 24q^{31} + 7q^{36} + 20q^{39} - 24q^{46} + 53q^{48} - 76q^{49} - 42q^{52} - 32q^{54} + 32q^{55} - 10q^{58} + 6q^{64} + 72q^{70} + 68q^{72} - 8q^{73} + 13q^{78} + 12q^{81} + 18q^{82} - 4q^{87} - 66q^{94} + 11q^{96} + O(q^{100}) \)

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.b.a \(6\) \(4.408\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
552.2.b.b \(6\) \(4.408\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(1+\cdots)q^{6}+\cdots\)
552.2.b.c \(80\) \(4.408\) None \(0\) \(0\) \(0\) \(0\)