Properties

Label 46.3.b
Level $46$
Weight $3$
Character orbit 46.b
Rep. character $\chi_{46}(45,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 46.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(46, [\chi])\).

Total New Old
Modular forms 14 4 10
Cusp forms 10 4 6
Eisenstein series 4 0 4

Trace form

\( 4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9} - 8 q^{12} - 4 q^{13} + 16 q^{16} - 16 q^{18} + 52 q^{23} + 16 q^{24} - 132 q^{25} - 64 q^{26} + 44 q^{27} + 84 q^{29} + 116 q^{31} + 56 q^{35} - 48 q^{36} - 60 q^{39} + 20 q^{41} + 56 q^{46} - 28 q^{47} - 16 q^{48} - 148 q^{49} + 176 q^{50} - 8 q^{52} - 104 q^{54} - 56 q^{55} - 80 q^{58} - 184 q^{59} - 24 q^{62} + 32 q^{64} + 4 q^{69} + 288 q^{70} - 100 q^{71} - 32 q^{72} - 148 q^{73} + 308 q^{75} + 344 q^{77} + 56 q^{78} + 68 q^{81} - 48 q^{82} - 120 q^{85} - 164 q^{87} + 104 q^{92} - 140 q^{93} + 136 q^{94} + 352 q^{95} + 32 q^{96} - 400 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(46, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
46.3.b.a 46.b 23.b $4$ $1.253$ 4.0.613376.1 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+2q^{4}+\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(46, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)