Properties

Label 8.10.a
Level 8
Weight 10
Character orbit a
Rep. character \(\chi_{8}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 10
Trace bound 3

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 8.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(8))\).

Total New Old
Modular forms 11 2 9
Cusp forms 7 2 5
Eisenstein series 4 0 4

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

\(2\)Dim.
\(+\)\(1\)
\(-\)\(1\)

Trace form

\(2q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 564q^{5} \) \(\mathstrut +\mathstrut 5904q^{7} \) \(\mathstrut -\mathstrut 31142q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 564q^{5} \) \(\mathstrut +\mathstrut 5904q^{7} \) \(\mathstrut -\mathstrut 31142q^{9} \) \(\mathstrut +\mathstrut 97560q^{11} \) \(\mathstrut -\mathstrut 188836q^{13} \) \(\mathstrut +\mathstrut 227120q^{15} \) \(\mathstrut -\mathstrut 171228q^{17} \) \(\mathstrut -\mathstrut 53720q^{19} \) \(\mathstrut +\mathstrut 957504q^{21} \) \(\mathstrut -\mathstrut 2602704q^{23} \) \(\mathstrut +\mathstrut 2675326q^{25} \) \(\mathstrut -\mathstrut 216496q^{27} \) \(\mathstrut +\mathstrut 1154940q^{29} \) \(\mathstrut -\mathstrut 5041088q^{31} \) \(\mathstrut -\mathstrut 5352352q^{33} \) \(\mathstrut +\mathstrut 24483936q^{35} \) \(\mathstrut -\mathstrut 13132788q^{37} \) \(\mathstrut -\mathstrut 11273872q^{39} \) \(\mathstrut -\mathstrut 15066924q^{41} \) \(\mathstrut +\mathstrut 45379928q^{43} \) \(\mathstrut +\mathstrut 10617052q^{45} \) \(\mathstrut -\mathstrut 79274400q^{47} \) \(\mathstrut +\mathstrut 43184626q^{49} \) \(\mathstrut +\mathstrut 29265040q^{51} \) \(\mathstrut +\mathstrut 39751980q^{53} \) \(\mathstrut -\mathstrut 188304496q^{55} \) \(\mathstrut +\mathstrut 67197088q^{57} \) \(\mathstrut +\mathstrut 173485944q^{59} \) \(\mathstrut -\mathstrut 12522052q^{61} \) \(\mathstrut -\mathstrut 84460080q^{63} \) \(\mathstrut -\mathstrut 241267032q^{65} \) \(\mathstrut +\mathstrut 195391624q^{67} \) \(\mathstrut -\mathstrut 85728064q^{69} \) \(\mathstrut +\mathstrut 335441808q^{71} \) \(\mathstrut -\mathstrut 7997164q^{73} \) \(\mathstrut -\mathstrut 118666760q^{75} \) \(\mathstrut -\mathstrut 366658368q^{77} \) \(\mathstrut -\mathstrut 34286944q^{79} \) \(\mathstrut +\mathstrut 323563378q^{81} \) \(\mathstrut -\mathstrut 291672408q^{83} \) \(\mathstrut +\mathstrut 886884952q^{85} \) \(\mathstrut -\mathstrut 187171344q^{87} \) \(\mathstrut -\mathstrut 6641100q^{89} \) \(\mathstrut -\mathstrut 1756556064q^{91} \) \(\mathstrut +\mathstrut 479023360q^{93} \) \(\mathstrut +\mathstrut 1902684144q^{95} \) \(\mathstrut +\mathstrut 204662980q^{97} \) \(\mathstrut -\mathstrut 1565047496q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(8))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
8.10.a.a \(1\) \(4.120\) \(\Q\) None \(0\) \(-60\) \(-2074\) \(-4344\) \(+\) \(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b \(1\) \(4.120\) \(\Q\) None \(0\) \(68\) \(1510\) \(10248\) \(-\) \(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)