Properties

Label 555.2.bx
Level $555$
Weight $2$
Character orbit 555.bx
Rep. character $\chi_{555}(22,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $456$
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.bx (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 960 456 504
Cusp forms 864 456 408
Eisenstein series 96 0 96

Trace form

\( 456 q + 36 q^{8} + O(q^{10}) \) \( 456 q + 36 q^{8} + 48 q^{14} + 36 q^{17} + 60 q^{20} + 36 q^{25} - 48 q^{30} - 24 q^{35} + 24 q^{37} - 168 q^{38} - 48 q^{39} - 60 q^{41} + 360 q^{44} - 48 q^{48} - 48 q^{49} - 204 q^{50} - 60 q^{52} + 36 q^{53} + 72 q^{57} - 48 q^{58} + 72 q^{60} - 144 q^{61} + 48 q^{62} - 228 q^{64} - 36 q^{65} - 24 q^{67} + 120 q^{70} - 96 q^{71} - 180 q^{73} - 60 q^{74} - 120 q^{76} + 36 q^{77} + 72 q^{78} + 96 q^{79} - 264 q^{80} + 120 q^{83} - 240 q^{86} - 216 q^{88} + 24 q^{89} + 48 q^{91} - 72 q^{93} - 72 q^{94} + 12 q^{95} - 72 q^{97} + 180 q^{98} + O(q^{100}) \)

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.bx.a 555.bx 185.z $456$ $4.432$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$

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

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