Properties

Label 92.2.e
Level $92$
Weight $2$
Character orbit 92.e
Rep. character $\chi_{92}(9,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $20$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 150 20 130
Cusp forms 90 20 70
Eisenstein series 60 0 60

Trace form

\( 20q + 2q^{3} + 2q^{5} + 2q^{7} - 4q^{9} + O(q^{10}) \) \( 20q + 2q^{3} + 2q^{5} + 2q^{7} - 4q^{9} - 2q^{11} + 6q^{13} - 17q^{15} - 9q^{17} - 11q^{19} - 47q^{21} - 22q^{23} - 16q^{25} - 19q^{27} - q^{29} - 13q^{31} - 5q^{33} + 14q^{35} + 34q^{37} + 30q^{39} + 28q^{41} + 44q^{43} + 78q^{45} + 26q^{47} + 60q^{49} + 62q^{51} + 14q^{53} + 26q^{55} + 3q^{57} - 10q^{59} - 56q^{61} - 27q^{63} - 87q^{65} - 44q^{67} - 51q^{69} - 37q^{71} - 12q^{73} - 53q^{75} - 47q^{77} - 6q^{79} - 10q^{81} - 25q^{83} + 8q^{85} + 48q^{87} + 10q^{89} + 26q^{91} - 14q^{93} + 29q^{95} - q^{97} - q^{99} + O(q^{100}) \)

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.e.a \(20\) \(0.735\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(2\) \(2\) \(2\) \(q+(1-\beta _{6}+\beta _{8}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(92, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(92, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)