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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
92.2.b.a \(4\) \(0.735\) \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+2\beta _{1}q^{4}+\cdots\)
92.2.b.b \(6\) \(0.735\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)