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Properties

Label 555.2.bh
Level $555$
Weight $2$
Character orbit 555.bh
Rep. character $\chi_{555}(122,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
Newform subspaces $1$
Sturm bound $152$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.bh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(555, [\chi])\).

Total New Old
Modular forms 320 320 0
Cusp forms 288 288 0
Eisenstein series 32 32 0

Trace form

\( 288 q - 4 q^{3} - 4 q^{7} + O(q^{10}) \) \( 288 q - 4 q^{3} - 4 q^{7} - 16 q^{10} - 26 q^{12} - 12 q^{13} - 30 q^{15} + 112 q^{16} - 48 q^{18} - 4 q^{21} + 12 q^{22} - 20 q^{25} - 64 q^{27} - 44 q^{28} - 36 q^{30} + 6 q^{33} - 80 q^{36} + 44 q^{37} - 32 q^{40} + 36 q^{42} + 8 q^{46} - 136 q^{48} - 48 q^{52} + 24 q^{55} - 54 q^{57} - 12 q^{58} - 36 q^{63} + 44 q^{70} + 138 q^{72} - 48 q^{73} - 8 q^{75} - 96 q^{76} - 12 q^{78} - 24 q^{81} - 208 q^{85} + 108 q^{87} - 82 q^{90} + 192 q^{91} + 78 q^{93} + 96 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(555, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
555.2.bh.a 555.bh 555.ah $288$ $4.432$ None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$