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Properties

Label 92.2.b
Level $92$
Weight $2$
Character orbit 92.b
Rep. character $\chi_{92}(91,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(92, [\chi])\).

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

Trace form

\( 10 q - 4 q^{2} + q^{6} - q^{8} - 10 q^{9} + O(q^{10}) \) \( 10 q - 4 q^{2} + q^{6} - q^{8} - 10 q^{9} + 7 q^{12} - 4 q^{13} - 16 q^{16} + 13 q^{18} + 8 q^{24} - 6 q^{25} - 23 q^{26} + 20 q^{29} + 16 q^{32} - 33 q^{36} - 12 q^{41} + 12 q^{46} + 39 q^{48} - 14 q^{49} + 36 q^{50} + 3 q^{52} + 29 q^{54} - 35 q^{58} + 25 q^{62} - 21 q^{64} - 12 q^{69} - 56 q^{70} + 43 q^{72} - 4 q^{73} - 56 q^{77} - 55 q^{78} + 58 q^{81} + 45 q^{82} + 56 q^{85} - 24 q^{92} + 8 q^{93} - 27 q^{94} - 73 q^{96} - 28 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(92, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
92.2.b.a 92.b 92.b $4$ $0.735$ \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+2\beta _{1}q^{4}+\cdots\)
92.2.b.b 92.b 92.b $6$ $0.735$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)