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Properties

Label 805.2.bi
Level $805$
Weight $2$
Character orbit 805.bi
Rep. character $\chi_{805}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1440$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.bi (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(805, [\chi])\).

Total New Old
Modular forms 2000 1440 560
Cusp forms 1840 1440 400
Eisenstein series 160 0 160

Trace form

\( 1440 q - 8 q^{3} + 16 q^{6} + O(q^{10}) \) \( 1440 q - 8 q^{3} + 16 q^{6} - 32 q^{12} + 16 q^{13} + 192 q^{16} - 72 q^{18} - 36 q^{23} + 8 q^{25} - 8 q^{27} + 40 q^{32} - 44 q^{33} - 208 q^{36} - 88 q^{37} - 32 q^{41} + 80 q^{46} - 192 q^{47} - 24 q^{48} + 56 q^{50} + 64 q^{52} - 56 q^{55} - 88 q^{57} + 24 q^{62} - 352 q^{66} + 16 q^{70} - 344 q^{71} + 48 q^{72} - 32 q^{73} - 144 q^{75} - 352 q^{76} - 40 q^{78} - 16 q^{81} + 96 q^{82} - 16 q^{85} + 16 q^{87} - 836 q^{90} - 112 q^{92} + 8 q^{93} - 56 q^{95} - 96 q^{96} + 132 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(805, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
805.2.bi.a 805.bi 115.l $1440$ $6.428$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$

Decomposition of \(S_{2}^{\mathrm{old}}(805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)