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Properties

Label 92.2.a
Level $92$
Weight $2$
Character orbit 92.a
Rep. character $\chi_{92}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(92))\).

Total New Old
Modular forms 15 2 13
Cusp forms 10 2 8
Eisenstein series 5 0 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(23\)FrickeDim
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{9} + 2 q^{11} - 6 q^{13} + 6 q^{15} - 2 q^{17} + 14 q^{21} - 6 q^{25} - 14 q^{27} - 10 q^{29} + 2 q^{31} - 6 q^{33} + 8 q^{35} + 10 q^{37} + 14 q^{39} - 6 q^{41} - 12 q^{45} + 18 q^{47} + 6 q^{49} - 18 q^{51} + 8 q^{53} - 4 q^{55} + 8 q^{57} - 12 q^{59} + 12 q^{61} - 28 q^{63} + 10 q^{65} + 22 q^{67} - 4 q^{69} - 18 q^{71} - 10 q^{73} - 2 q^{75} - 8 q^{77} - 16 q^{79} + 10 q^{81} + 14 q^{83} - 8 q^{85} + 18 q^{87} + 12 q^{89} + 18 q^{91} + 14 q^{93} + 4 q^{95} - 10 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(92))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 23
92.2.a.a 92.a 1.a $1$ $0.735$ \(\Q\) None 92.2.a.a \(0\) \(-3\) \(-2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
92.2.a.b 92.a 1.a $1$ $0.735$ \(\Q\) None 92.2.a.b \(0\) \(1\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(92))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(92)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)