Properties

Label 552.2.t
Level $552$
Weight $2$
Character orbit 552.t
Rep. character $\chi_{552}(19,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
Newform subspaces $2$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.t (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1000 480 520
Cusp forms 920 480 440
Eisenstein series 80 0 80

Trace form

\( 480q + 4q^{2} - 8q^{4} + 4q^{6} + 4q^{8} - 48q^{9} + O(q^{10}) \) \( 480q + 4q^{2} - 8q^{4} + 4q^{6} + 4q^{8} - 48q^{9} - 8q^{16} + 4q^{18} + 4q^{24} - 48q^{25} + 4q^{32} - 22q^{34} + 14q^{36} - 110q^{38} + 22q^{40} - 110q^{42} + 154q^{44} - 48q^{46} + 88q^{48} - 48q^{49} - 70q^{50} + 110q^{52} - 18q^{54} + 110q^{56} - 22q^{58} + 22q^{60} + 80q^{62} - 8q^{64} + 4q^{72} - 22q^{74} - 110q^{76} - 198q^{80} - 48q^{81} - 52q^{82} - 220q^{86} - 176q^{88} - 186q^{92} - 190q^{94} + 4q^{96} - 156q^{98} + O(q^{100}) \)

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.t.a \(240\) \(4.408\) None \(0\) \(24\) \(0\) \(0\)
552.2.t.b \(240\) \(4.408\) None \(4\) \(-24\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)