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Properties

Label 285.2.bh
Level $285$
Weight $2$
Character orbit 285.bh
Rep. character $\chi_{285}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $240$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.bh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).

Total New Old
Modular forms 528 240 288
Cusp forms 432 240 192
Eisenstein series 96 0 96

Trace form

\( 240 q - 12 q^{6} - 12 q^{7} + O(q^{10}) \) \( 240 q - 12 q^{6} - 12 q^{7} - 36 q^{16} + 120 q^{20} - 48 q^{21} + 24 q^{22} + 24 q^{23} - 24 q^{25} - 24 q^{26} - 72 q^{28} - 12 q^{32} - 12 q^{33} - 12 q^{36} - 132 q^{38} - 132 q^{40} - 72 q^{41} - 108 q^{43} + 24 q^{47} + 24 q^{51} + 36 q^{53} - 24 q^{57} - 144 q^{58} + 48 q^{60} + 24 q^{61} - 168 q^{62} - 144 q^{67} - 48 q^{68} - 48 q^{70} - 72 q^{72} - 36 q^{73} - 48 q^{76} - 216 q^{77} + 120 q^{78} + 24 q^{80} + 144 q^{82} - 12 q^{83} + 72 q^{85} + 96 q^{86} - 48 q^{87} + 360 q^{88} + 36 q^{90} + 72 q^{91} - 48 q^{92} + 24 q^{95} + 48 q^{96} + 96 q^{97} + 192 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(285, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.bh.a 285.bh 95.r $240$ $2.276$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(285, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(285, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)