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Properties

Label 555.2.bg
Level $555$
Weight $2$
Character orbit 555.bg
Rep. character $\chi_{555}(236,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $208$
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.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{12})\)
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 320 208 112
Cusp forms 288 208 80
Eisenstein series 32 0 32

Trace form

\( 208 q + O(q^{10}) \) \( 208 q - 24 q^{13} + 96 q^{16} - 20 q^{18} + 16 q^{19} + 36 q^{21} + 32 q^{22} + 56 q^{24} - 168 q^{28} - 32 q^{31} - 8 q^{34} - 80 q^{37} + 28 q^{39} - 44 q^{42} + 32 q^{43} + 16 q^{45} - 160 q^{49} + 84 q^{51} + 72 q^{52} - 112 q^{54} + 16 q^{55} + 36 q^{57} + 28 q^{60} - 56 q^{61} - 40 q^{63} - 84 q^{66} - 24 q^{69} - 48 q^{72} - 40 q^{76} - 72 q^{78} - 72 q^{79} - 16 q^{81} - 64 q^{82} - 112 q^{84} - 16 q^{87} - 56 q^{88} + 160 q^{91} - 24 q^{93} - 40 q^{94} - 12 q^{96} - 88 q^{97} - 36 q^{99} + O(q^{100}) \)

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.bg.a 555.bg 111.m $208$ $4.432$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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