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Properties

Label 555.2.bp
Level $555$
Weight $2$
Character orbit 555.bp
Rep. character $\chi_{555}(4,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
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.bp (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{18})\)
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 480 240 240
Cusp forms 432 240 192
Eisenstein series 48 0 48

Trace form

\( 240 q + 12 q^{5} + O(q^{10}) \) \( 240 q + 12 q^{5} + 36 q^{14} + 12 q^{19} - 30 q^{20} + 12 q^{21} - 48 q^{25} - 36 q^{26} + 24 q^{30} + 48 q^{34} + 12 q^{35} - 264 q^{36} + 36 q^{39} + 66 q^{40} - 144 q^{41} + 192 q^{44} + 24 q^{46} - 12 q^{49} + 42 q^{50} - 6 q^{55} - 36 q^{59} + 108 q^{61} - 276 q^{64} - 66 q^{65} + 12 q^{69} - 42 q^{70} - 24 q^{71} - 108 q^{74} + 96 q^{76} - 96 q^{79} + 24 q^{84} - 12 q^{85} + 72 q^{86} - 300 q^{89} + 6 q^{90} + 72 q^{91} - 48 q^{94} - 42 q^{95} + 120 q^{96} + 12 q^{99} + O(q^{100}) \)

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.bp.a 555.bp 185.v $240$ $4.432$ None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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