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Properties

Label 88.2.a
Level $88$
Weight $2$
Character orbit 88.a
Rep. character $\chi_{88}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 88 = 2^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 88.a (trivial)
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 \(M_{2}(\Gamma_0(88))\).

Total New Old
Modular forms 16 3 13
Cusp forms 9 3 6
Eisenstein series 7 0 7

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

\(2\)\(11\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(-\)\(+\)$-$\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3 q - 2 q^{3} - 4 q^{7} + 9 q^{9} + O(q^{10}) \) \( 3 q - 2 q^{3} - 4 q^{7} + 9 q^{9} - 3 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 4 q^{19} - 12 q^{21} + 10 q^{23} + 7 q^{25} - 2 q^{27} - 10 q^{29} - 14 q^{31} + 2 q^{33} + 20 q^{35} - 12 q^{37} + 16 q^{39} + 10 q^{41} - 22 q^{45} + 8 q^{47} + 19 q^{49} + 20 q^{51} + 10 q^{53} - 16 q^{57} - 6 q^{59} - 2 q^{61} - 32 q^{63} - 20 q^{65} + 10 q^{67} + 10 q^{69} - 2 q^{71} + 18 q^{73} - 36 q^{75} + 4 q^{77} - 12 q^{79} - 5 q^{81} + 8 q^{83} + 24 q^{85} + 40 q^{87} + 8 q^{89} - 32 q^{91} + 26 q^{93} - 24 q^{95} + 20 q^{97} - 9 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(88))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11
88.2.a.a 88.a 1.a $1$ $0.703$ \(\Q\) None \(0\) \(-3\) \(-3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-3q^{5}-2q^{7}+6q^{9}-q^{11}+\cdots\)
88.2.a.b 88.a 1.a $2$ $0.703$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(88))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(88)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)