Properties

Label 552.2.u
Level $552$
Weight $2$
Character orbit 552.u
Rep. character $\chi_{552}(17,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $240$
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.u (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
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 1040 240 800
Cusp forms 880 240 640
Eisenstein series 160 0 160

Trace form

\( 240q - 4q^{9} + O(q^{10}) \) \( 240q - 4q^{9} - 16q^{25} + 12q^{27} - 8q^{31} + 44q^{37} + 20q^{39} + 44q^{43} + 124q^{49} + 12q^{55} + 16q^{69} - 74q^{75} - 144q^{81} + 24q^{85} - 170q^{87} + 12q^{93} - 198q^{99} + O(q^{100}) \)

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.u.a \(240\) \(4.408\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)