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Properties

Label 552.2.bb
Level $552$
Weight $2$
Character orbit 552.bb
Rep. character $\chi_{552}(13,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
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.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
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 480 520
Cusp forms 920 480 440
Eisenstein series 80 0 80

Trace form

\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} + O(q^{10}) \) \( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(552, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
552.2.bb.a 552.bb 184.p $480$ $4.408$ None \(4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{22}]$

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

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