Properties

Label 552.2.j
Level $552$
Weight $2$
Character orbit 552.j
Rep. character $\chi_{552}(323,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $4$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 100 88 12
Cusp forms 92 88 4
Eisenstein series 8 0 8

Trace form

\( 88q - 3q^{6} + O(q^{10}) \) \( 88q - 3q^{6} - 8q^{10} - 13q^{12} - 8q^{16} + 21q^{18} + 4q^{22} + 20q^{24} + 88q^{25} - 12q^{27} + 12q^{28} - 22q^{30} - 8q^{33} + 12q^{34} - q^{36} + 8q^{40} - 8q^{42} + 32q^{43} + 5q^{48} - 104q^{49} + 40q^{51} - 2q^{52} + 20q^{54} - 8q^{57} - 42q^{58} - 24q^{60} - 18q^{64} - 14q^{66} + 48q^{70} - 72q^{72} - 16q^{73} - 56q^{75} + 44q^{76} - 35q^{78} + 8q^{81} + 54q^{82} - 14q^{84} - 12q^{88} - 46q^{90} + 48q^{91} + 2q^{94} - 77q^{96} + 32q^{97} + 64q^{99} + O(q^{100}) \)

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.j.a \(2\) \(4.408\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(-8\) \(0\) \(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}-4q^{5}+\cdots\)
552.2.j.b \(2\) \(4.408\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(8\) \(0\) \(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}+4q^{5}+\cdots\)
552.2.j.c \(42\) \(4.408\) None \(0\) \(2\) \(-8\) \(0\)
552.2.j.d \(42\) \(4.408\) None \(0\) \(2\) \(8\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(552, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)