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Properties

Label 555.2.cc
Level $555$
Weight $2$
Character orbit 555.cc
Rep. character $\chi_{555}(53,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $864$
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.cc (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{36})\)
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 960 960 0
Cusp forms 864 864 0
Eisenstein series 96 96 0

Trace form

\( 864 q - 18 q^{3} - 48 q^{6} - 24 q^{7} + O(q^{10}) \) \( 864 q - 18 q^{3} - 48 q^{6} - 24 q^{7} - 12 q^{10} + 36 q^{12} - 24 q^{13} - 36 q^{15} - 48 q^{16} - 54 q^{18} - 24 q^{21} - 48 q^{22} - 72 q^{25} + 18 q^{27} + 48 q^{30} - 48 q^{31} - 24 q^{33} - 48 q^{36} - 276 q^{40} - 54 q^{42} - 48 q^{43} - 102 q^{45} - 48 q^{46} + 30 q^{48} - 12 q^{51} + 12 q^{52} - 108 q^{55} - 60 q^{57} + 96 q^{58} - 42 q^{60} - 72 q^{61} - 6 q^{63} - 120 q^{66} - 36 q^{67} + 72 q^{70} + 144 q^{72} + 72 q^{75} - 120 q^{76} - 102 q^{78} - 60 q^{81} - 12 q^{82} + 60 q^{85} - 246 q^{87} - 132 q^{88} - 24 q^{90} - 24 q^{91} - 102 q^{93} - 300 q^{96} + 12 q^{97} + O(q^{100}) \)

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.cc.a 555.cc 555.bc $864$ $4.432$ None \(0\) \(-18\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{36}]$