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Properties

Label 555.2.t
Level $555$
Weight $2$
Character orbit 555.t
Rep. character $\chi_{555}(253,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
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 160 76 84
Cusp forms 144 76 68
Eisenstein series 16 0 16

Trace form

\( 76 q - 4 q^{2} + 76 q^{4} - 8 q^{5} - 12 q^{8} + O(q^{10}) \) \( 76 q - 4 q^{2} + 76 q^{4} - 8 q^{5} - 12 q^{8} + 4 q^{10} + 8 q^{13} + 8 q^{14} + 76 q^{16} - 20 q^{20} + 4 q^{25} - 16 q^{26} - 16 q^{28} + 28 q^{29} - 16 q^{30} - 8 q^{31} - 28 q^{32} - 28 q^{35} - 28 q^{37} + 56 q^{38} - 4 q^{40} + 32 q^{43} - 4 q^{45} - 96 q^{46} + 16 q^{48} + 40 q^{50} - 8 q^{51} + 56 q^{52} + 12 q^{53} + 72 q^{56} - 76 q^{58} - 4 q^{60} - 4 q^{61} - 32 q^{62} + 28 q^{64} + 24 q^{65} + 32 q^{66} + 16 q^{67} - 8 q^{69} + 16 q^{70} - 32 q^{71} + 60 q^{73} + 20 q^{74} - 16 q^{75} - 48 q^{76} - 8 q^{77} - 48 q^{78} - 32 q^{79} - 60 q^{80} - 76 q^{81} - 192 q^{86} - 28 q^{89} - 48 q^{91} + 48 q^{93} + 24 q^{94} - 24 q^{95} + O(q^{100}) \)

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.t.a 555.t 185.k $76$ $4.432$ None \(-4\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(555, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(555, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)