Properties

Label 88.2.a
Level 88
Weight 2
Character orbit a
Rep. character \(\chi_{88}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(88))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11
88.2.a.a \(1\) \(0.703\) \(\Q\) None \(0\) \(-3\) \(-3\) \(-2\) \(+\) \(+\) \(q-3q^{3}-3q^{5}-2q^{7}+6q^{9}-q^{11}+\cdots\)
88.2.a.b \(2\) \(0.703\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(3\) \(-2\) \(-\) \(+\) \(q+\beta q^{3}+(2-\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots\)

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

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