Properties

Label 555.2.bz
Level $555$
Weight $2$
Character orbit 555.bz
Rep. character $\chi_{555}(56,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $600$
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.bz (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
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 960 600 360
Cusp forms 864 600 264
Eisenstein series 96 0 96

Trace form

\( 600 q + O(q^{10}) \) \( 600 q + 96 q^{16} - 36 q^{21} - 60 q^{24} + 48 q^{28} - 24 q^{31} - 120 q^{34} + 12 q^{37} - 48 q^{43} - 24 q^{45} + 36 q^{49} - 120 q^{51} + 120 q^{54} - 72 q^{57} + 24 q^{61} - 72 q^{63} - 120 q^{66} - 132 q^{69} - 492 q^{72} - 432 q^{78} + 144 q^{79} - 96 q^{81} + 72 q^{82} - 84 q^{84} - 144 q^{87} - 108 q^{91} + 72 q^{93} + 144 q^{94} + 324 q^{96} + 48 q^{97} + 36 q^{99} + O(q^{100}) \)

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.bz.a 555.bz 111.q $600$ $4.432$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$

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

\( S_{2}^{\mathrm{old}}(555, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)